# Examples for test
#
# find_2f1 finds hypergeometric solutions of all differential 
# operators in the lists Linp, LLinp, and the operator ALinp below.
#
# The list Linp contains non-logarithmic examples.
# The list LLinp contains logarithmic examples.
# ALinp is an example where pullback function is algebraic.
# 
# Then 
# type find_2f1( Linp[i] ) 
# where i=1,...,n, such that n := nops(Linp),
# or 
# type find_2f1( LLinp[i] ) 
# where i=1,...,m, such that m := nops(LLinp),
# or 
# type find_2f1( ALinp ).

Linp :=
[100*(x^2-4*x+5)*(2*x-5)*x*Dx^2+(520*x^3-2580*x^2+4200*x-2000)*Dx+78*x^2-267*x+240,
100*(2*x+1)*(x ^2+1)*(x-2)*Dx^2+(520*x^3-540*x^2+120*x-240)*Dx+78*x^2-45*x+18,
49*(4*x^2-13*x+32)*(8*x-13)*Dx^2+( 3024*x^2-9828*x+12187)*Dx+240*x-390,
2*x*(x^2-2)*Dx^2+(5*x^2-3)*Dx+x, 81*(x+3)*(x+1)*(x-3)*x*Dx^2+
(234*x^3+234*x^2-918*x-486)*Dx+52*x^2+52*x-48,
144*(x^2+2)*(2*x-1)*(x+4)*Dx^2+(816*x^3+2184*x^2-96
*x+1344)*Dx+170*x^2+315*x-20,
144*(x^2+2)*(2*x-1)*(x+4)*Dx^2+(816*x^3+2184*x^2-96*x+1344)*Dx+170*x
^2+315*x-20, 441*(x^2+27)*x*Dx^2+(966*x^2+10206)*Dx+136*x,
49*x*(9*x^2-8)*Dx^2+(777*x^2-168)*Dx+55 *x,
441*(x-9)*(x^2+3)*(3*x+1)*Dx^2+(3150*x^3-17472*x^2+4158*x-29484)*Dx+300*x^2-728*x+396,
49*x*(3 *x+7)*(3*x-7)*Dx^2+(945*x^2-1029)*Dx+95*x,
441*(8*x^2-49)*x*Dx^2+(7560*x^2-15435)*Dx+760*x, 8*(x^2
-3)*x*Dx^2+18*(x-1)*(x+1)*Dx+3*x, 4*(x-1)*(x+1)*(x^2+1)*Dx^2+12*Dx*x^3+3*x^2,
25*x*(x-1)*(x+1)*Dx^ 2+(60*x^2-20)*Dx+12*x,
25*x*(x-1)*(x+1)*Dx^2+(60*x^2-20)*Dx+12*x, 49*x*(x-1)*(x+1)*Dx^2+(119*x^2-\
35)*Dx+24*x, 27*(x^2+3)*x*Dx^2+(66*x^2+72)*Dx+14*x,
64*(x+4)*(x-2)*x*(3*x-4)*Dx^2+(528*x^3+96*x^2-\ 2368*x+1280)*Dx+99*x^2-30*x-120,
9*(x+4)*(x-2)*(3*x-4)*Dx^2+(63*x^2+12*x-192)*Dx+9*x-4, 100*x*(2*x
-1)*(x+4)*Dx^2+10*(x+2)*(35*x-4)*Dx+25*x+4,
16*(x-2)*(x+1)*(x+2)*(x-1)*Dx^2+8*x*(7*x^2-17)*Dx+21*( x-1)*(x+1),
4*(7*x+2)*(7*x+3)*(7*x-6)*Dx^2+(3136*x^2-140*x-456)*Dx+455*x+45,
8*x*(2*x-1)*(x+4)*Dx^ 2+(38*x^2+84*x-20)*Dx+7*x+5,
256*(3*x+10)*x*(15*x-4)*(x+4)*Dx^2+(30240*x^3+164160*x^2+182784*x-\
25600)*Dx+4725*x^2+17910*x+6000,
441*(x-2)*(x+25)*x*Dx^2+(987*x^2+15414*x-18900)*Dx+133*x+855, 441
*(x-2)*(x+25)*x*Dx^2+(924*x^2+14406*x-18900)*Dx+76*x+504,
49*(x-2)*(3*x+250)*x*Dx^2+(287*x^2+15344 *x-17500)*Dx+17*x+310,
25*(2*x-5)*(x-4)*x*(6*x+1)*Dx^2+(780*x^3-3570*x^2+3250*x+200)*Dx+117*x^2-\
330*x+60,
25*(6*x-1)*x*(2*x+5)*(x+4)*Dx^2+(960*x^3+4440*x^2+4000*x-350)*Dx+288*x^2+840*x+210,
49*x
*(12*x-121)*(33*x-2)*(x-6)*Dx^2+(44352*x^3-508998*x^2+1308356*x-47432)*Dx+3168*x^2-21570*x+10570,
20*(5*x+28)*(5*x+12)*(2*x-5)*Dx^2+(2150*x^2+8420*x-4720)*Dx+190*x+449,
576*(9*x-34)*(5*x+8)*(11*x+
14)*(x-2)*Dx^2+(736560*x^3-1576128*x^2-2020992*x+2463360)*Dx+107415*x^2-147658*x-172072,
36*(x+8)*
(9*x-28)*(5*x+22)*(13*x-40)*Dx^2+(56160*x^3+248676*x^2-959700*x-1059744)*Dx+9360*x^2+24748*x-\
120481,
196*(8*x+35)*(x-5)*(5*x-21)*(3*x+13)*Dx^2+(57120*x^3-4956*x^2-1136072*x-159740)*Dx+6120*x^
2+1947*x-85875,
49*(54*x+31)*(2*x-3)*(32*x-13)*Dx^2+(362880*x^2-398916*x-53466)*Dx+36480*x-30045,
784*(14+3*x)*(8*x-77)*(15*x+22)*(11*x+46)*Dx^2+(7318080*x^3+15253560*x^2-174317472*x-436357152)*Dx
+653400*x^2+2272905*x-1716870,
441*(7*x-32)*(8*x+15)*(128*x-103)*Dx^2+(7074816*x^2-17832360*x-\
11502981)*Dx+808192*x-1150062,
196*(9*x^2-66*x-7)*(2*x-3)*x*Dx^2+(8568*x^3-50484*x^2+36848*x+588)*
Dx+918*x^2-2709*x+210,
64*(12*x^2-1)*(3*x-1)*(3*x+1)*Dx^2+96*x*(198*x^2-19)*Dx+3564*x^2-207, 81*(2
*x-1)*(x^2+2*x-2)*(x+4)*Dx^2+(468*x^3+1944*x^2+702*x-1260)*Dx+104*x^2+292*x-40,
256*(x+8)*(9*x-88)
*(11*x^2+56*x+44)*Dx^2+(66528*x^3+255232*x^2-2209664*x-6093824)*Dx+10395*x^2+45320*x-57220,
81*(44
*x^2-60*x+3)*(-9+4*x)*x*Dx^2+(39600*x^3-99468*x^2+49788*x-729)*Dx+7700*x^2-10857*x+819,
400*(x^2+ 998*x+169)*x*Dx^2+(920*x^2+618760*x+54080)*Dx+133*x+33040,
36*(65219*x^2+37394*x-1417)*(28*x-1)*Dx
^2+(134612016*x^2+40847856*x-1629984)*Dx+15019004*x+108097,
121*(27*x+19)*(1331*x^2-134*x-529)*Dx^
2+(11068596*x^2+4251060*x-1823184)*Dx+2475660*x+623100,
64*x*(x^2+5*x+5)*Dx^2+(112*x^2+400*x+240)* Dx+8*x+15,
4*(x^2-x-1)*(x+2)*(x-2)*Dx^2+(12*x^3-12*x^2-28*x+16)*Dx+3*x^2-3*x-3,
8*x*(20*x^2+20*x+1)*Dx^2+(272*x^2+176*x+4)*Dx+18*x+3,
16*(5*x^2-1)*(2*x+1)*Dx^2+(360*x^2+120*x-24)*Dx+60*x+15, 196*(
x^2+2576*x+64)*x*Dx^2+(392*x^2+721280*x+10752)*Dx+45*x+26280,
25*(x^2-44*x-2)*x*Dx^2+(50*x^2-1375* x-25)*Dx+4*x-25,
16*(x^2+6*x-15)*(4*x+9)*(5*x-9)*Dx^2+(800*x^3+3432*x^2-6960*x-3672)*Dx+100*x^2+
213*x-573,
16*(x^2+6*x-15)*(4*x+9)*(5*x-9)*Dx^2+(800*x^3+3432*x^2-6960*x-3672)*Dx+100*x^2+213*x-\
573,
4*(5*x^2-16*x-160)*(2*x-5)*(4*x+17)*Dx^2+(480*x^3-232*x^2-11200*x-6400)*Dx+120*x^2+58*x-1413,
36*(8*x+3)*(7*x^2-1)*Dx^2+(3552*x^2+1080*x-96)*Dx+200*x+65,
36*(x^2+2*x-27)*(4*x+25)*x*Dx^2+(336*x
^3+2268*x^2-264*x-8100)*Dx+28*x^2+147*x-70,
441*(x+24)*(2*x-1)*(7*x^2-14*x+6)*Dx^2+(13524*x^3+
169932*x^2-330330*x+131796)*Dx+644*x^2+2338*x-2332,
1764*(2*x-25)*(2*x+39)*(52*x^2-26*x-597)*Dx^2+
(847392*x^3+3136224*x^2-108119424*x+19585188)*Dx+65572*x^2+59150*x-2941601,
9*(2*x-9)*(20*x^2+86*x
+83)*(2*x+7)*Dx^2+(1680*x^3+5712*x^2-6528*x-23382)*Dx+140*x^2+490*x+189,
784*(4+7*x)*(9*x-4)*(5*x^
2+x-1)*Dx^2+(582120*x^3+169960*x^2-118888*x-16352)*Dx+51975*x^2+13355*x-7355,
16*x*(34391*x^2+7910 *x-1)*Dx^2+(903992*x^2+135600*x-8)*Dx+54043*x+935,
225*(x-1)*x*(756*x^2-756*x+125)*Dx^2+30*(2*x-1)
*(8316*x^2-8316*x+625)*Dx+116424*x^2-116424*x+18536,
16*x*(28*x^2-1281*x+3)*Dx^2+(864*x^2-24888*x+ 24)*Dx+76*x-361,
441*x*(6*x-49)*(2*x^2-9*x-3)*Dx^2+(11844*x^3-105042*x^2+191268*x+46305)*Dx+705*x^
2-3575*x+675,
144*(7986*x^2+8061*x-47233)*(29+9*x)*Dx^2+(21274704*x^2+65226072*x-4424856)*Dx+
2595450*x+6015295,
16*(3087*x^2-37730*x+19800)*(9*x-4)*Dx^2+(857304*x^2-6879600*x+3150400)*Dx+
46431*x-110110,
64*(x-4)*(5*x^2+4*x+4)*x*Dx^2+(880*x^3-1888*x^2-832*x-384)*Dx+165*x^2-180*x-24,
36 *(x+4)*(9*x^2+6*x+5)*Dx^2+(792*x^2+2640*x+888)*Dx+133*x+248,
100*(2*x+1)*(x^2-2*x+5)*x*Dx^2+(520*x ^3-540*x^2+800*x+100)*Dx+78*x^2-45*x+10,
25*(x^2+2*x+5)*(2*x-1)*x*Dx^2+(160*x^3+170*x^2+275*x-75)* Dx+48*x^2+30*x+15,
196*(x-11)*(x^2+4)*Dx^2+(476*x^2-3696*x+560)*Dx+75*x-315, 25*(2*x-1)*(5*x^2+6*x
+2)*Dx^2+(675*x^2+315*x-45)*Dx+180*x+48,
9*x*(x^2-10*x+27)*Dx^2+(18*x^2-120*x+162)*Dx+2*x-7, 9*(3*
x^2-10*x+9)*x*Dx^2+(54*x^2-120*x+54)*Dx+6*x-7,
4*(8*x+3)*(4*x^2-4*x+3)*Dx^2+(240*x^2-128*x+60)*Dx+ 20*x-7,
9*(2*x+1)*(x^2+2)*(2*x-1)*Dx^2+15*x*(8*x^2+7)*Dx+40*x^2+12,
9*(x-2)*(x+2)*(2*x^2+1)*Dx^2+ 15*x*(4*x^2-7)*Dx+20*x^2-12,
9*(x^2-2*x+3)*(4*x+3)*(x+1)*Dx^2+(96*x^3-6*x^2-3*x+72)*Dx+(8*x+5)*(2* x-1),
36*(x^2+2*x+3)*(x-1)*(4*x-3)*Dx^2+(336*x^3+12*x^2-24*x-252)*Dx+28*x^2-5*x-11,
9*(x-2)*(2*x-3)*(x^2+4*x+12)*Dx^2+(60*x^3+12*x^2+6*x-360)*Dx+20*x^2-2*x-16,
484*(3*x^2+8*x+8)*(4*x-5)*(8*x-9)*Dx
^2+(156288*x^3+18480*x^2-183920*x-68288)*Dx+53280*x^2-2940*x-36645,
9*(32*x+13)*(27*x^2-10*x+1)*Dx ^2+(17172*x^2-228*x-528)*Dx+2565*x-200,
1764*x*(2187*x^2+2846*x+3267)*Dx^2+(9185400*x^2+7650048*x+
3841992)*Dx+1524339*x+554948, 4*(x^3-2)*x*Dx^2+(12*x^3-4)*Dx+3*x^2,
9*(x+1)*(x^2-x+1)*Dx^2+18*Dx*x ^2+2*x, 16*(x^3+4)*x*Dx^2+(56*x^3+48)*Dx+21*x^2,
98*x*(18*x^3+49)*Dx^2+(4788*x^3+686)*Dx+855*x^2,
49*x*(8*x^3-49)*Dx^2+(1064*x^3-1372)*Dx+190*x^2,
36*(13*x+17)*(x^2-14*x+481)*(4*x+9)*Dx^2+(4368*x^
3-32100*x^2+807816*x+1247292)*Dx+364*x^2-1549*x+2835,
1600*(x-1)*x*(5376*x^2-7152*x+2401)*Dx^2+(
21073920*x^3-37943040*x^2+20250320*x-2881200)*Dx+2370816*x^2-3012336*x+884745,
196*(3*x-14)*(3*x^2
+9*x+7)*(3*x+2)*Dx^2+(12852*x^3-2268*x^2-61908*x-45864)*Dx+1377*x^2+891*x-963,
36*(49*x-60)*(147*x
^2-44*x+12)*Dx^2+(493920*x^2-519456*x+75456)*Dx+24255*x-12980,
144*(3*x+5)*(5*x+3)*(3*x^2-4*x+3)*
Dx^2+(18360*x^3+11880*x^2-9384*x+5256)*Dx+3825*x^2+1380*x-895,
441*x*(378*x^2-454*x+343)*Dx^2+( 349272*x^2-276486*x+100842)*Dx+28728*x-10792,
784*(5*x^2+1)*(20*x-19)*(60*x-41)*Dx^2+(14448000*x^3
-17472000*x^2+6058920*x-1189440)*Dx+3870000*x^2-3039000*x+444075,
225*(x-2)*(280*x^2+48*x+9)*(5*x-\
7)*Dx^2+(966000*x^3-2395200*x^2+1205895*x+102510)*Dx+257600*x^2-445760*x+96704,
400*(x-7)*(7*x^2+7
*x+8)*(x-8)*Dx^2+(7560*x^3-85120*x^2+197560*x+98880)*Dx+1323*x^2-11270*x+12803,
400*(7*x^2-7*x+8)*
(x+7)*(x+8)*Dx^2+(7560*x^3+85120*x^2+197560*x-98880)*Dx+1323*x^2+11270*x+12803,
18*(7*x-11)*(126*x ^2+147*x+43)*Dx^2+(31752*x^2-8568*x-15792)*Dx+3773*x+539,
7*(x-7)*(847*x^2-686*x+163)*Dx^2+(12705* x^2-77322*x+29301)*Dx+1815*x-6468,
1089*x*(8*x^2-50*x+121)*(14*x-27)*Dx^2+(391776*x^3-2340096*x^2+
4888092*x-2371842)*Dx+118720*x^2-447280*x+410120,
225*x*(24*x^2+232*x+675)*(42*x+1)*Dx^2+(695520*x
^3+4763520*x^2+8161530*x+101250)*Dx+185472*x^2+743232*x+216928,
16*x*(9*x^2-15*x+40)*(x+1)*Dx^2+( 360*x^3-120*x^2+288*x+256)*Dx+45*x^2,
x*(2*x-1)*(18*x^2+15*x+20)*Dx^2+2*(3*x-1)*(18*x^2+9*x+7)*Dx+ 27*x^2,
16*(784*x^2+161*x+61)*(7*x-5)*Dx^2+(194432*x^2-83048*x-7624)*Dx+25200*x-7821,
1764*(x+42)*
(901*x^2+22001*x+137494)*(x-14)*Dx^2+(4162620*x^3+187297992*x^2+945906192*x-8700532512)*Dx+644215*
x^2+24204453*x+112641494,
225*(28*x^2+196*x+663)*(7*x-29)*(91*x+123)*Dx^2+(11771760*x^3+41983200*x
^2+22510320*x-264845070)*Dx+2746744*x^2+8031688*x+6896554,
144*(x+1)*(10*x^2-13*x+169)*(26*x+17)*
Dx^2+(106080*x^3+48480*x^2+596904*x+530088)*Dx+22100*x^2+12380*x+9685,
4*(-68+3*x)*(11*x^2+403*x+
7436)*(39*x-869)*Dx^2+(15444*x^3-159480*x^2-3867372*x-8257392)*Dx+3861*x^2-47646*x-626403,
(16*x^3 +48*x^2-90*x+34)*Dx^2+(32*x^2+64*x-60)*Dx+3*x+1,
16*(x^3-3*x+6)*(3*x+7)*Dx^2+(120*x^3+224*x^2-168* x-80)*Dx+15*x^2+21*x-22,
4*(8*x^3-3*x^2+24*x+8)*(4*x+1)*Dx^2+(384*x^3-16*x^2+448*x+128)*Dx+96*x^2+ 4*x+9,
(192*x^3+117*x^2-66*x+7)*Dx^2+(384*x^2+156*x-44)*Dx+45*x,
(192*x^3+117*x^2-66*x+7)*Dx^2+( 384*x^2+156*x-44)*Dx+45*x,
(588*x^3+44100*x^2-23520*x+3136)*Dx^2+(1176*x^2+58800*x-15680)*Dx+99*x+ 1485,
25*(x^3-16*x^2+77*x+2)*x*Dx^2+(80*x^3-920*x^2+2695*x+25)*Dx+24*x^2-168*x+105,
4*(4*x^3+7*x^2 -8*x-16)*(2*x-3)*Dx^2+8*x*(12*x^2+x-28)*Dx+24*x^2-2*x-33,
4*(2*x+3)*(4*x^3-7*x^2-8*x+16)*Dx^2+8*x* (12*x^2-x-28)*Dx+24*x^2+2*x-33,
64*(5*x-4)*(x^3+2*x^2+3*x+4)*Dx^2+(720*x^3+736*x^2+688*x+576)*Dx+
45*x^2+38*x+23,
16*(2*x-1)*(2*x^3+11*x^2-4*x+7)*Dx^2+(192*x^3+720*x^2-456*x+216)*Dx+48*x^2+120*x-\
39, 25*(x^3-3*x-3)*(3*x-4)*Dx^2+(210*x^3-200*x^2-330*x+20)*Dx+42*x^2-24*x-38,
25*(x^3-3*x+3)*(3*x+ 4)*Dx^2+(210*x^3+200*x^2-330*x-20)*Dx+42*x^2+24*x-38,
(49*x^3-8967*x+48657)*Dx^2+(98*x^2-5978)*Dx+ 6*x-8,
(13068*x^3+6776*x^2-8228*x+1936)*Dx^2+(35640*x^2+12320*x-7480)*Dx+8295*x+1120,
676*(2*x^3+
19*x^2+24*x-169)*x*Dx^2+(4888*x^3+34580*x^2+28704*x-96668)*Dx+1974*x^2+9177*x+1386,
25*(x-4)*(6*x^
3-22*x^2-12*x-9)*Dx^2+(420*x^3-2540*x^2+3160*x+870)*Dx+84*x^2-372*x+194,
25*(6*x^3+22*x^2-12*x+9)*
(x+4)*Dx^2+(420*x^3+2540*x^2+3160*x-870)*Dx+84*x^2+372*x+194,
(36*x^3-4032*x^2+19152*x-25704)*Dx^2 +(72*x^2-5376*x+12768)*Dx+5*x-140,
1764*x*(24*x^3+13*x^2+18*x-3)*Dx^2+(94752*x^3+31668*x^2+16632*x
+1764)*Dx+5640*x^2+715*x-126,
196*(6*x^3+21*x^2+6*x-26)*(18*x-5)*Dx^2+(46872*x^3+118188*x^2+5124*x
-68460)*Dx+2511*x^2+4572*x-1035,
(3136*x^3+4116*x^2-8736*x+3136)*Dx^2+(6720*x^2+5880*x-6240)*Dx+ 960*x+105,
1225*(x+4)*(14*x^3-14*x^2+20*x-25)*Dx^2+(55860*x^3+122500*x^2-69160*x+52150)*Dx+17556*x
^2+24332*x-7414,
(4*x-1)*(400*x^3+140*x^2+56*x+35)*Dx^2+(4400*x^3+220*x^2+70*x+28)*Dx+825*x^2,
64*
(71*x^3-870*x^2+32175*x+64220)*(x+4)*Dx^2+(12496*x^3-70464*x^2+2239920*x+8232640)*Dx+2343*x^2-7086
*x+59799]:

LLinp := [Dx^2+1/4*(x^2-12)/(x^2+4)^2, Dx^2+1/4*(x^2-x+1)/(x-1)^2/x^2,
Dx^2+3/8*(6*x^2-3*x+2)/x^2/(3*x-2)^2 ,
Dx^2+27/4*(27*x^2-36*x+64)/(9*x+4)^2/(3*x-4)^2,
Dx^2+1/144*(32*x^2+23*x+27)/x^2/(x+1)^2, Dx^2-5/
36*(875*x^6-2350*x^4-3545*x^2+292)/(5*x^2+1)^2/(5*x^2-4)^2,
Dx^2+1/4*(x^4-14*x^3+85*x^2-348*x+648) /x^2/(x^2-10*x+27)^2,
Dx^2+3/4*(27*x^4-126*x^3+75*x^2-720*x+1024)/x^2/(9*x^2-33*x+64)^2, Dx^2-1/4*
(7920*x^10+43968*x^8+46744*x^6+8400*x^4-20121*x^2-1336)/(12*x^4+8*x^2-1)^2/(3*x^2+8)^2,
Dx^2-3/4*(
189*x^6-1134*x^5+1647*x^4+972*x^3-2817*x^2+666*x-67)/(3*x^2-6*x+1)^2/(9*x^2-18*x+1)^2,
Dx^2+1/16*( 23*x^3+4)/(x-1)^2/(x^2+x+1)^2/x^2,
Dx^2+1/16*(41*x^3-5)/(x-1)^2/(x^2+x+1)^2/x^2, Dx^2+1/4*(12*x^2-\
27*x+16)/(x-1)^2/(3*x-4)^2/x^2, Dx^2+(18*x^2-40*x+23)/(4*x-5)^2/(x-1)^2/(x+1)^2,
Dx^2+(18*x^2+4*x+ 1)/x^2/(x-2)^2/(4*x+1)^2,
Dx^2-1/36*(28*x^6-164*x^4+179*x^2-70)/(x-1)^2/(x+1)^2/(2*x^2-1)^2, Dx^2+
1/36*(36*x^6+36*x^4-83*x^2+38)/(x-1)^2/(x+1)^2/(2*x^2-1)^2,
Dx^2+1/4*(5*x^4+10*x^3+36*x^2-16*x+16) /x^2/(x+2)^2/(3*x-2)^2,
Dx^2-1/36*(7*x^4-28*x^3+8*x^2+40*x-36)/(x-1)^2/x^2/(x-2)^2, Dx^2+1/4*(9*x^
4-36*x^3+90*x^2-20*x+5)/(3*x-1)^2/(x-3)^2/x^2,
Dx^2+1/4*(49*x^4+294*x^3+2296*x^2-4878*x+2431)/(x+7)^2/(x-1)^2/(7*x-5)^2,
Dx^2+1/8*(64*x^4-113*x^3+90*x^2-40*x+8)/(2*x-1)^2/(3*x-2)^2/x^2, Dx^2+1/36*
(81*x^4-270*x^3+405*x^2-339*x+128)/(x-1)^2/(3*x-4)^2/x^2,
Dx^2+1/4*(405*x^4-540*x^3+1296*x^2+384*x +256)/x^2/(9*x+4)^2/(3*x-4)^2,
Dx^2+1/36*(230400*x^4-56200*x^3+9780*x^2-264*x+5)/(5*x-1)^2/(32*x-1)^2/x^2,
Dx^2-1/4*(12375*x^10-96270*x^8+260503*x^6-290868*x^4+134076*x^2-45184)/(x^2-2)^2/(3*x^2-1)^2/(15*x^2-32)^2,
Dx^2+1/4*(5*x^6-30*x^5+96*x^4-184*x^3+240*x^2-192*x+64)/(3*x^2-6*x+4)^2/x^2/(x-\
2)^2,
Dx^2-1/36*(7*x^6+336*x^5+3552*x^4-29696*x^3-503040*x^2-577536*x-524288)/(x^2+16*x+16)^2/(x+
16)^2/x^2,
Dx^2+1/36*(9*x^6-126*x^5+783*x^4-2790*x^3+5805*x^2-6425*x+3200)/x^2/(x-4)^2/(x^2-5*x+5)
^2,
Dx^2-4*(9*x^6+66*x^5+457*x^4-412*x^3-4293*x^2-2598*x-5517)/(x-1)^2/(x+1)^2/(9*x^2+48*x+199)^2,
Dx^2-1/36*(16*x^6-224*x^5+1092*x^4-1960*x^3-180*x^2+4025*x-3600)/(x-4)^2/(x^2-5*x+5)^2/x^2,
Dx^2+1
/9*(36*x^6-128*x^5+196*x^4-278*x^3+227*x^2-52*x+8)/x^2/(4*x-1)^2/(x^2-2*x+2)^2,
Dx^2+1/36*(36*x^6+
72*x^5-144*x^4+972*x^3+945*x^2+350*x-175)/x^2/(x^2+2*x+5)^2/(2*x-1)^2,
Dx^2-1/36*(64*x^6+128*x^5+
644*x^4-972*x^3-945*x^2+450*x-225)/x^2/(x^2+2*x+5)^2/(2*x-1)^2,
Dx^2+1/144*(432*x^6+2073*x^5-3196*
x^4+902*x^3-97*x^2-293*x+27)/x^2/(3*x-1)^2/(x^3-2*x^2+x-1)^2,
Dx^2+1/144*(1764*x^6-4655*x^5+17388*
x^4+195398*x^3+69304*x^2+1425*x+32)/(7*x^2-42*x-1)^2/(x+1)^2/x^2,
Dx^2+1/72*(263538*x^6-227601*x^5
+298870*x^4-77066*x^3-9012*x^2-521*x+16)/x^2/(11*x^2-8*x-1)^2/(11*x-1)^2,
Dx^2+1/16*(12845056*x^6-\
35323904*x^5+44713984*x^4-27360256*x^3+7418756*x^2-680161*x-19152)/(x-1)^2/(16*x-7)^2/(112*x^2-35*
x+4)^2,
Dx^2-1/36*(74809606144*x^14+107303927808*x^12+59992055808*x^10+17427324160*x^8+2879964555*
x^6+277833927*x^4+15202849*x^2+395469)/(64*x^2+27)^2/(7*x^2+1)^2/(64*x^4+19*x^2+1)^2,
Dx^2-2*(8*x^
8-96*x^7+294*x^6+128*x^5-690*x^4-1827*x^3+414*x^2-216*x-162)/x^2/(x-4)^2/(6*x^3-22*x^2-12*x-9)^2,
Dx^2+3/4*(12*x^8+96*x^7+148*x^6-240*x^5-1713*x^4-3680*x^3-3264*x^2-768*x+256)/(x+2)^2/(2*x^3+3*x+4)^2/(3*x+4)^2,
Dx^2+1/36*(36*x^8-144*x^7+288*x^6-360*x^5+845*x^4-1258*x^3+777*x^2-184*x-85)/(2*x-1)^2/(x^2-x+1)^2/(x^2-x-1)^2,
Dx^2-1/16*(45*x^8-504*x^7-5418*x^6+24420*x^5+105765*x^4-419700*x^3-\
2688400*x^2-4982000*x-3290000)/(3*x^3-45*x-50)^2/(x-10)^2/(x+2)^2,
Dx^2+1/8*(50*x^8+200*x^7+120*x^
6+11239*x^5-1544*x^4-22368*x^3-42336*x^2+96768*x-41472)/(5*x-6)^2/(x^3+4*x^2+12*x-18)^2/x^2,
Dx^2-\
5/4*(150000*x^8+420000*x^7-39000*x^6-959000*x^5-479825*x^4+565600*x^3+404180*x^2-83680*x-101044)/(
10*x^2+25*x+16)^2/(5*x^2-2)^2/(10*x-7)^2,
Dx^2+5/4*(262144*x^8-466944*x^7+9127936*x^6-16018360*x^5
+40711515*x^4-55215532*x^3+28196092*x^2-6201888*x+550240)/(32*x^3-3*x^2-246*x+26)^2/(24*x-7)^2/(2*
x-1)^2,
Dx^2+1/4*(2160900*x^8-2646000*x^7-616260*x^6+2497312*x^5-2369283*x^4+1180092*x^3-348268*x^
2+57792*x-5760)/(10*x^2-8*x+3)^2/(147*x^2-44*x+12)^2/x^2,
Dx^2+1/4*(4*x^10+8*x^9+140*x^7-71*x^6-84
*x^5-42*x^4+168*x^3-111*x^2+30*x-3)/x^2/(2*x-1)^2/(x^4+2*x^3+3*x^2-4*x+1)^2,
Dx^2-1/9*(160*x^10-\
1920*x^9+13020*x^8-55138*x^7+159936*x^6-306264*x^5+360808*x^4-164340*x^3-130545*x^2+155736*x-62208)/x^2/(x^3-4*x^2+10*x-6)^2/(4*x^2-13*x+32)^2,
Dx^2-1/9*(160*x^10+1920*x^9+13020*x^8+55138*x^7+
159936*x^6+306264*x^5+360808*x^4+164340*x^3-130545*x^2-155736*x-62208)/x^2/(x^3+4*x^2+10*x+6)^2/(4
*x^2+13*x+32)^2,
Dx^2-1/36*(640*x^10+5120*x^9-374432*x^8-682240*x^7+46114432*x^6-40291264*x^5-\
953331392*x^4+21716806904*x^3-274623300536*x^2-20764756896*x+2031333316623)/(x^4-78*x^2+91*x-1209)
^2/(2*x+39)^2/(2*x-25)^2,
Dx^2-1/4*(18370800*x^10-40240800*x^9-1187191080*x^8+4500873216*x^7+
13517591283*x^6-90024115230*x^5+69947168760*x^4+420124294800*x^3-1164940131600*x^2+1184473668000*x
-444088960000)/(36*x^3-315*x+350)^2/(135*x^2+252*x-980)^2/(x-2)^2,
Dx^2-2*(2*x^12-96*x^11+954*x^10
+36200*x^9-1304490*x^8+19939278*x^7-185336959*x^6+1249037436*x^5-7461537420*x^4+41972325220*x^3-\
182107591659*x^2+472961270112*x-525423837903)/(3*x-22)^2/(x^3-183*x+993)^2/(x^3-16*x^2+57*x+137)^2
,
Dx^2-1/4*(5103*x^12-30618*x^11-140697*x^10+211572*x^9+2104542*x^8-1427004*x^7-9881586*x^6-\
11379600*x^5-5510757*x^4+1582438*x^3+3588891*x^2+1636524*x+241192)/(9*x^4-30*x^2-56*x-23)^2/(x^2-4
*x-2)^2/(9*x+1)^2,
Dx^2-3/4*(27216*x^12+54432*x^11-686232*x^10+1235520*x^9+4226553*x^8-8818146*x^7
-7123212*x^6+40800168*x^5-54707040*x^4+33545472*x^3-4304640*x^2-5222400*x+2269184)/(9*x-4)^2/(12*x
^3-21*x+34)^2/(3*x^3+6*x^2-12*x+8)^2,
Dx^2-1/4*(81920*x^12-245760*x^11-184320*x^10+749056*x^9-\
370944*x^8-346752*x^7+297024*x^6-34560*x^5-80112*x^4+23272*x^3+3612*x^2-1764*x+147)/x^2/(8*x^3-4*x
^2-4*x+1)^2/(32*x^3-48*x^2-24*x+7)^2,
Dx^2-3/4*(622080*x^12+4976640*x^11+11679552*x^10-2528064*x^9
-38756016*x^8-19032192*x^7+42327180*x^6+12478356*x^5-22335003*x^4+6966384*x^3-4543266*x^2+2288700*
x-441835)/(6*x^3+21*x^2+6*x-26)^2/(18*x-5)^2/(6*x^3+9*x^2-6*x-1)^2,
Dx^2-7*(29647548*x^12+
178591182*x^11-405015086*x^10-633455830*x^9+1860895050*x^8+3425708384*x^7-8541479639*x^6+
6600250902*x^5-2191150885*x^4-271487930*x^3+503344821*x^2-155943956*x+15753743)/(63*x^2+294*x-89)^
2/(49*x^4-84*x^2+98*x-27)^2/(7*x-1)^2,
Dx^2+7/4*(148237740*x^12+638834070*x^11-8709605891*x^10-\
45827377988*x^9-48997780839*x^8+170918133428*x^7+551003713946*x^6+706659839424*x^5+516904856006*x^
4+237518161286*x^3+70046680137*x^2+12523527604*x+1053011989)/(49*x^4+714*x^2+392*x-3)^2/(126*x^2+
147*x+43)^2/(7*x+5)^2,
Dx^2-7/9*(299769652*x^12+1288021252*x^11-7678664511*x^10-98861362278*x^9-\
57481229337*x^8+1667236776660*x^7+4895487158016*x^6-6998493193692*x^5-44661561313824*x^4-\
41558097273056*x^3+134636240963497*x^2-144615660803250*x-434765787811407)/(49*x^4-546*x^2-1274*x+
1248)^2/(28*x^2+196*x+663)^2/(7*x-29)^2,
Dx^2+1/36*(793881*x^14+411642*x^13+2702051*x^12-1165428*x
^11-9256731*x^10+7642206*x^9+6013965*x^8-10163592*x^7+3168151*x^6+2316654*x^5-2522751*x^4+1073484*
x^3-251592*x^2+32256*x-1792)/x^2/(11*x^4-11*x^2+6*x-1)^2/(27*x^3+14*x^2-17*x+4)^2,
Dx^2-(14080*x^
16-84480*x^15+144384*x^14+361728*x^13-2057856*x^12+3095424*x^11+2039168*x^10-14574528*x^9+20999040
*x^8-3790816*x^7-28578432*x^6+44413680*x^5-33339512*x^4+18942312*x^3-15455880*x^2+10584684*x-\
2863863)/(2*x-3)^2/(4*x^4-4*x^2+16*x+1)^2/(12*x^4-16*x^3-12*x^2+72*x-69)^2,
Dx^2-3/4*(16*x^6-40*x^ 4+17*x^2-5)/(x-1)^2/(2*x+1)^2/(2*x-1)^2/(x+1)^2,
Dx^2-2*(10*x^9+37*x^6+180*x^3+81)/x^2/(x+1)^2/(x^ 2-x+1)^2/(x^3+9)^2,
Dx^2+1/8*(408*x^4-1012*x^3+948*x^2-399*x+64)/(3*x-2)^2/x^2/(4*x-3)^2/(2*x-1)^2 ,
Dx^2+1/8*(2520*x^4+17183*x^3+43509*x^2+55149*x+39103)/(x-1)^2/(5*x+13)^2/(2*x+7)^2/(x+1)^2,
Dx^2
-1/4*(20*x^6+60*x^5-3*x^4-114*x^3-75*x^2-5)/x^2/(2*x-1)^2/(2*x+3)^2/(x+1)^2,
Dx^2-3/4*(x^10+18*x^8
+25*x^6-76*x^4-540*x^2+32)/(x-1)^2/(x+1)^2/(x^2+8)^2/(x^2+2)^2,
Dx^2-2*(162*x^6+648*x^5-27*x^4-\
2388*x^3-2145*x^2-450*x-800)/x^2/(x-1)^2/(3*x+5)^2/(9*x+16)^2,
Dx^2-1/9*(2268*x^6+27958*x^5-28627*
x^4+6332*x^3+1768*x^2+1600*x-144)/(9*x+4)^2/(x^2-2*x+2)^2/(4*x-1)^2/x^2,
Dx^2+1/36*(52435*x^6-\
471848*x^5+2136579*x^4-1224248*x^3+150985*x^2-7200*x+225)/x^2/(x^2-18*x+1)^2/(5*x-1)^2/(x-5)^2,
Dx
^2+1/36*(77435*x^6+17372*x^5+23663*x^4-40808*x^3+4913*x^2-148*x+5)/(x+1)^2/(5*x-1)^2/(x^2-18*x+1)^
2/x^2,
Dx^2+1/16*(7483392*x^6-10764544*x^5+6640832*x^4-2161921*x^3+451444*x^2-58016*x+3136)/(x-1)^
2/(16*x-7)^2/(112*x^2-35*x+4)^2/x^2,
Dx^2-7/12*(13388358316032*x^14-41030308988928*x^12+
51945911748864*x^10-35632025056768*x^8+14455963448976*x^6-3510761899176*x^4+479508054039*x^2-\
28884349791)/(14*x-9)^2/(14*x+9)^2/(7*x^2-3)^2/(2352*x^4-1624*x^2+243)^2,
Dx^2-7/36*(
1765470306250000*x^14-488505119025000*x^12-3830714046075*x^10+3564241702175*x^8-186267676350*x^6+
3464715030*x^4-23903495*x^2+119907)/(7*x+1)^2/(7*x-1)^2/(875*x^2-27)^2/(980*x^4-35*x^2-1)^2,
Dx^2+
(x^8+8*x^7+34*x^6+84*x^5+42*x^4-168*x^3-8*x^2+80*x-20)/(x+4)^2/(2*x-1)^2/(x^2+2*x-2)^2/x^2,
Dx^2+(
x^8+8*x^7+34*x^6+106*x^5+119*x^4-212*x^3-120*x^2+192*x-48)/x^2/(2*x-1)^2/(x+4)^2/(x^2+2*x-2)^2,
Dx
^2+1/36*(5*x^8+35*x^7-24*x^6+90*x^5+601*x^4+768*x^3+424*x^2+144*x+36)/(x^2-x-1)^2/(x+1)^2/(x+2)^2/
x^2,
Dx^2+1/36*(9*x^8+63*x^7+35*x^6+80*x^5+400*x^4+488*x^3+256*x^2+80*x+20)/(x^2-x-1)^2/(x+1)^2/(x
+2)^2/x^2,
Dx^2+(45*x^8-180*x^7+238*x^6-84*x^5+159*x^4-388*x^3+354*x^2-144*x+16)/(9*x^2-9*x+8)^2/(
2*x-1)^2/(x-1)^2/x^2,
Dx^2+(49*x^8+1176*x^7+29442*x^6-38598*x^5-145365*x^4+403956*x^3-377392*x^2+
153600*x-23040)/x^2/(2*x-1)^2/(7*x^2-14*x+6)^2/(x+24)^2,
Dx^2+1/4*(64*x^8-3584*x^7+153232*x^6-\
1031124*x^5+893973*x^4+196632*x^3+21404*x^2+800*x+20)/x^2/(x-3)^2/(x^2-44*x-2)^2/(8*x+1)^2,
Dx^2-1
/36*(64*x^8-3072*x^7+51108*x^6-320092*x^5+197763*x^4+4434144*x^3-17588240*x^2+21772800*x-10497600)
/(2*x-27)^2/(x-1)^2/x^2/(x^2-16*x+40)^2,
Dx^2+1/144*(80*x^8-320*x^7+944*x^6-1712*x^5+1320*x^4-160*
x^3+95*x^2-247*x+36)/(x-1)^2/(2*x-1)^2/(x^2-x-1)^2/x^2,
Dx^2+1/144*(144*x^8-576*x^7+1360*x^6-2064*
x^5+1420*x^4-72*x^3+3*x^2-215*x+32)/(x-1)^2/(2*x-1)^2/(x^2-x-1)^2/x^2,
Dx^2-1/4*(696*x^8+3688*x^7+
1491*x^6-8470*x^5-809*x^4+6960*x^3-3832*x^2+1296*x-324)/x^2/(x^2+x-1)^2/(8*x^2+9*x-9)^2/(x-2)^2,
Dx^2+1/144*(800*x^8+16515*x^7+292597*x^6+1502943*x^5+2042793*x^4+1265193*x^3+527391*x^2-48843*x+
19683)/(x^2+14*x-3)^2/(x+1)^2/(5*x+9)^2/x^2,
Dx^2+1/16*(1600*x^8+4000*x^7+7540*x^6+18393*x^5+25683
*x^4+14208*x^3-992*x^2-4352*x-1280)/(x-1)^2/(4*x^2+7*x+4)^2/(5*x+4)^2/x^2,
Dx^2+1/4*(19600*x^8+
333200*x^7+6123460*x^6-8836394*x^5-13841995*x^4+38411200*x^3-31495800*x^2+11172000*x-1470000)/(2*x
-1)^2/(2*x+35)^2/(35*x^2-56*x+20)^2/x^2,
Dx^2-2/9*(71442*x^8-2000376*x^7+20209581*x^6-91308276*x^5
+140547015*x^4+282175902*x^3-1385059456*x^2+1969790976*x-1146617856)/x^2/(x-9)^2/(21*x-64)^2/(9*x^
2-57*x+64)^2,
Dx^2+1/144*(13789440*x^8+83054713*x^7+202281242*x^6+250860915*x^5+155941605*x^4+
25846695*x^3-24820263*x^2-15234642*x-2657205)/(x-1)^2/(35*x^2+63*x+27)^2/(9*x^2+17*x+9)^2/x^2,
Dx^
2-1/16*(65028096*x^8-140894208*x^7+18047232*x^6+92111232*x^5-14986448*x^4-15758239*x^3-3896340*x^2
-744800*x-78400)/(x-1)^2/(21*x+4)^2/x^2/(144*x^2-84*x-35)^2,
Dx^2-1/4*(3*x^10-54*x^9+393*x^8-1487*
x^7+3117*x^6-3456*x^5+1335*x^4+1053*x^3-1404*x^2+603*x-108)/x^2/(x-4)^2/(x-1)^2/(x^3-6*x^2+9*x-3)^
2,
Dx^2-1/4*(3*x^10+24*x^9+42*x^8-73*x^7-194*x^6+21*x^5+101*x^4+40*x^3-72*x^2+5*x-5)/x^2/(x-1)^2/(
x+3)^2/(x^3+3*x^2-1)^2,
Dx^2+1/4*(16*x^10-112*x^9+372*x^8-832*x^7+1408*x^6-1680*x^5+1233*x^4-504*x
^3+156*x^2-80*x+20)/(2*x-3)^2/(2*x^3-3*x^2+2)^2/x^2/(x-1)^2,
Dx^2-1/4*(20*x^10+312*x^9+12*x^8-\
14380*x^7-52845*x^6+68010*x^5+489337*x^4+107712*x^3-1668195*x^2-255150*x+1148175)/x^2/(4*x+9)^2/(x
^2+2*x-9)^2/(x^2+6*x-15)^2,
Dx^2+3/4*(300*x^10+37200*x^9+4679020*x^8+148921488*x^7-2084241921*x^6+
12898697220*x^5+33742832580*x^4+15621055200*x^3-114177826800*x^2-14823000000*x+30375000000)/(10*x^
3-84*x^2+45*x-90)^2/(x+18)^2/(3*x+250)^2/x^2,
Dx^2+1/144*(324*x^10-1728*x^9+4320*x^8-5049*x^7+1494
*x^6+1449*x^5-156*x^4-1223*x^3+1042*x^2-425*x+32)/(x^3-2*x^2+x-1)^2/(x-1)^2/x^2/(3*x-1)^2,
Dx^2+1/
4*(5120*x^10-2560*x^9+18432*x^8-5120*x^7-6464*x^6-672*x^5+3104*x^4+584*x^3-168*x^2-48*x-3)/x^2/(2*
x-1)^2/(6*x+1)^2/(8*x^3-6*x-1)^2,
Dx^2+1/36*(12800*x^10+2304000*x^9+495891120*x^8-23727130600*x^7+
24235975077*x^6+24978981480*x^5+229663582067*x^4-122870990328*x^3+164740434327*x^2+42644973240*x-\
4082348583)/(4*x-43)^2/(5*x^2+1)^2/(2*x+3)^2/(x^2+208*x-119)^2,
Dx^2+1/36*(20736*x^10-110592*x^9+
327456*x^8-546696*x^7+587529*x^6-520902*x^5+314673*x^4-78500*x^3-14340*x^2+10880*x-1600)/x^2/(6*x-\
5)^2/(x-2)^2/(8*x^3-3*x^2-2*x+1)^2,
Dx^2-1/9*(28672*x^10+401408*x^9+2449408*x^8+7968768*x^7+
14001536*x^6+10963712*x^5-1996032*x^4-9363680*x^3-4991825*x^2-458750*x-31250)/(8*x^2+28*x+25)^2/(8
*x^2+12*x+1)^2/(2*x+5)^2/x^2,
Dx^2-1/36*(466560*x^10-16329600*x^9+223711632*x^8-1485071712*x^7+
4595232600*x^6-3690990360*x^5-9071604125*x^4+11496212028*x^3-7504272678*x^2-317652300*x-259416045)
/(6*x-49)^2/x^2/(2*x^2-9*x-3)^2/(9*x^2-78*x+49)^2,
Dx^2-1/4*(7*x^12-70*x^11+969*x^10-3392*x^9+
20069*x^8-20670*x^7+97275*x^6+264372*x^5-116604*x^4+1845648*x^3-17748*x^2-125280*x-248832)/(3*x^2-\
3*x+32)^2/(x^3+9*x+6)^2/(x-3)^2/x^2,
Dx^2+1/144*(432*x^12-9699*x^11+44672*x^10-93540*x^9+135033*x^
8-163360*x^7+145623*x^6-73665*x^5+15971*x^4-4599*x^3+216*x^2-2727*x+243)/x^2/(x^3-2*x^2+x-1)^2/(3*
x-1)^2/(x^3-2*x^2+x+3)^2,
Dx^2-1/144*(1728*x^12-12096*x^11+36288*x^10-60048*x^9+48517*x^8+7730*x^7
-55221*x^6+48796*x^5-18022*x^4+1797*x^3-302*x^2+545*x-36)/(x-1)^2/(4*x-1)^2/(x^4-3*x^3+3*x^2-x-1)^
2/x^2,
Dx^2-1/4*(4096*x^12-4096*x^11+22528*x^10-30208*x^9+43648*x^8-55960*x^7+40388*x^6-37052*x^5+
19511*x^4-8176*x^3+4186*x^2-1372*x+147)/(2*x-1)^2/(x^2+1)^2/(24*x^3-4*x^2+28*x-7)^2/x^2,
Dx^2-1/36
*(4302592*x^12-14137088*x^11+43292480*x^10-23081856*x^9+498779920*x^8-539658160*x^7+786289180*x^6-\
798370192*x^5+599574328*x^4-29245644*x^3+732844163*x^2-7746272*x+155553202)/(14*x-1)^2/(2*x^2+1)^2
/(7*x^2+8*x+10)^2/(4*x^2-12*x+17)^2,
Dx^2+1/4*(457656598268100*x^12-11390564223561600*x^11+
112713056278944660*x^10-383238406615693552*x^9+10064412425869725*x^8+3827968870537765800*x^7-\
11099985849798426000*x^6+15355304875501920000*x^5-12381163548213600000*x^4+6137009413920000000*x^3
-1849006906560000000*x^2+311624755200000000*x-22581504000000000)/x^2/(9*x-4)^2/(3087*x^2-37730*x+
19800)^2/(770*x^3-3696*x^2+3465*x-900)^2,
Dx^2+3/4*(3728499221049901056*x^12+8848499039037554688*x
^11+18006723779699736576*x^10+1801064378557813248*x^9-1056491338455312912*x^8-331558022815736832*x
^7-45471945702863592*x^6-3692516029464672*x^5-192240605454777*x^4-6506558120592*x^3-138730349988*x
^2-1692615840*x-8991988)/(81*x+4)^2/(384*x+19)^2/(288*x^3+633*x^2+72*x+2)^2/(396*x^2-1)^2,
Dx^2+1/
4*(x^14-28*x^13+372*x^12-2760*x^11+10032*x^10-6240*x^9-61248*x^8+183936*x^7-368592*x^6+601920*x^5-\
778176*x^4+587520*x^3-746496*x^2+165888*x-248832)/(x^3-6*x^2-8)^2/(x^3-6*x^2-9)^2/(x-4)^2/x^2,
Dx^
2-4*(25*x^14-2120*x^13+60180*x^12-567220*x^11-1319821*x^10+39164628*x^9-218259966*x^8+349896408*x^
7-239593473*x^6-26320960*x^5+2259776*x^4+35201244*x^3-210923*x^2-27212*x-246)/(x-1)^2/(3*x^2-74*x-\
1)^2/(5*x-1)^2/(x^4-28*x^3+102*x^2+68*x+1)^2,
Dx^2-1/36*(243*x^14-16362*x^13+484353*x^12-8293854*x
^11+90959737*x^10-668193324*x^9+3336794643*x^8-11205279548*x^7+24042047181*x^6-27835617402*x^5+
3537708583*x^4+30663858186*x^3-29279247849*x^2+5953823136*x-530325387)/(3*x-19)^2/(x-9)^2/(x^3-11*
x^2+19*x-3)^2/(x^3-11*x^2+19*x-1)^2,
Dx^2-1/36*(243*x^14-1782*x^13+5643*x^12-15411*x^11+39514*x^10
-70080*x^9+104538*x^8-143810*x^7+133143*x^6-114903*x^5+78115*x^4-14913*x^3+6264*x^2+10395*x-972)/x
^2/(3*x-1)^2/(x^3-2*x^2+x-3)^2/(x^3-2*x^2+x-4)^2,
Dx^2-1/4*(768*x^14+1536*x^13+2688*x^12-6592*x^11
-5072*x^10-3744*x^9+22832*x^8+2560*x^7+1320*x^6-34576*x^5+19120*x^4+1212*x^3+243*x^2-1890*x+567)/x
^2/(x^2+2*x+3)^2/(4*x-3)^2/(4*x^4-4*x+3)^2,
Dx^2-1/9*(27040*x^14-378560*x^13+23358556*x^12+
87403890*x^11+1094519430*x^10+34921266054*x^9+120515300134*x^8+5254298328136*x^7+57162401212735*x^
6+225264073965450*x^5+449804575307997*x^4+1457898309636834*x^3+6042791268721051*x^2+
11771492899593076*x+8048676549168385)/(13*x+17)^2/(4*x+9)^2/(x^2-14*x+481)^2/(x^4+52*x^2+546*x+949)^2,
Dx^2-1/36*(2055208960*x^14+5578424320*x^13+17801986048*x^12+20237636608*x^11+21459883456*x^10
-9172077440*x^9-29296027808*x^8-34550468672*x^7-17664038084*x^6+13303758600*x^5+6128627760*x^4+
3169409040*x^3-1916388045*x^2-812671650*x+201952575)/(28*x+5)^2/(2*x+1)^2/(4*x^3+2*x^2+6*x-3)^2/(
32*x^3+13*x^2+50*x-35)^2,
Dx^2-2/9*(2*x^16-744*x^15+120747*x^14-10744614*x^13+523829370*x^12-\
9208916748*x^11-408788740859*x^10+29086047917322*x^9-727823236441884*x^8+7713140027359680*x^7-\
17228292120584187*x^6-1346312104995906*x^5-83775775224382*x^4-348012351276*x^3+2916742635*x^2+
19381950*x+28350)/x^2/(x-12)^2/(x^4-108*x^3+3254*x^2+228*x+1)^2/(x^3-109*x^2+3419*x+15)^2,
Dx^2-1/
36*(125440*x^16-1361920*x^15+3929520*x^14+16938236*x^13-147275417*x^12+309759288*x^11+558053192*x^
10-4254968480*x^9+8066174766*x^8+1036408240*x^7-33683805208*x^6+71718149796*x^5-83728335785*x^4+
78306723224*x^3-82511547072*x^2+70056874304*x-25249725440)/(8*x^3-x^2-36*x+112)^2/(x-2)^2/(7*x-19)
^2/(x^4-4*x^2+12*x+1)^2,
Dx^2+1/4*(24*x^6+54*x^5+51*x^4+54*x^3+40*x^2+16*x+4)/x^2/(x-1)^2/(2*x+1)^
2/(x+2)^2/(x+1)^2,
Dx^2+(30625*x^8+416500*x^7+3149650*x^6+20321520*x^5+95060928*x^4+213684480*x^3+
48473600*x^2-501760000*x-501760000)/x^2/(2*x-5)^2/(5*x+28)^2/(5*x+12)^2/(7*x+20)^2,
Dx^2+3*(6*x^10
+64*x^9+174*x^8+72*x^7-156*x^6-24*x^5+126*x^4+12*x^3-42*x^2+12*x-1)/x^2/(x+2)^2/(4*x-1)^2/(x-1)^2/
(x^3+3*x^2+3*x-1)^2,
Dx^2+1/4*(64*x^10-448*x^9+1488*x^8-2928*x^7+3432*x^6-2208*x^5+648*x^4-72*x^3+
48*x^2-36*x+9)/(2*x-3)^2/(2*x-1)^2/(2*x^2-2*x-1)^2/(x-1)^2/x^2,
Dx^2+1/36*(225*x^10+6750*x^9+
171185*x^8+1465728*x^7-3682*x^6+47588*x^5+2496318*x^4+465728*x^3+21185*x^2-5250*x-175)/x^2/(x^2+18
*x+1)^2/(5*x+1)^2/(x-1)^2/(x+5)^2,
Dx^2-1/9*(1792*x^10+7168*x^9+12736*x^8+2176*x^7-19392*x^6-24192
*x^5-11808*x^4-3240*x^3-1134*x^2-432*x-81)/x^2/(4*x+3)^2/(2*x+1)^2/(2*x-1)^2/(2*x^2+3*x+2)^2,
Dx^2
+2*(2982*x^10+42763*x^9+79055*x^8-633072*x^7-3121676*x^6+1816238*x^5+53157486*x^4+143441480*x^3+
130940110*x^2+30094575*x+30109275)/(x+21)^2/(x+3)^2/(7*x^2-15)^2/(x+5)^2/(x^2+7)^2,
Dx^2+1/8*(
13887000*x^10+143499215*x^9+45280458*x^8-1428013224*x^7-3152145606*x^6+11445213870*x^5+67709649690
*x^4+104231979600*x^3+50752646550*x^2+7613368875*x+16496282500)/(x+20)^2/(x+2)^2/(25*x^2-8*x-35)^2
/(5*x+19)^2/(x^2+5)^2,
Dx^2+1/36*(50000000*x^10+731359375*x^9+1217420625*x^8+345930750*x^7+
199506375*x^6+407992770*x^5+281343033*x^4+64773432*x^3+8368920*x^2+1166400*x+104976)/(4*x-1)^2/(5*
x^2+7*x+1)^2/x^2/(5*x+18)^2/(25*x+6)^2,
Dx^2+1/4*(36*x^12+1572*x^10-4144*x^9-73923*x^8+260616*x^7+
624016*x^6-3932928*x^5+3089664*x^4+13584384*x^3-34836480*x^2+31850496*x-10616832)/x^2/(3*x-4)^2/(x
+4)^2/(x-2)^2/(2*x^3-27*x+36)^2,
Dx^2-1/4*(7*x^12-140*x^11+1318*x^10-4556*x^9+649*x^8+16552*x^7+
54932*x^6-223672*x^5+239513*x^4+67108*x^3-312314*x^2+131524*x-17001)/(x^2-8*x+25)^2/(3*x+1)^2/(x-1)^2/(x-3)^2/(x^2+1)^2,
Dx^2-1/36*(448*x^12+21056*x^11+116928*x^10-4766880*x^9-37447620*x^8+
177215112*x^7-320050536*x^6+347584452*x^5-264742461*x^4+141683744*x^3-47576624*x^2+8087040*x-\
419904)/(x-1)^2/(2*x^2+34*x-27)^2/(4*x-1)^2/(x^2+16*x-8)^2/x^2,
Dx^2-1/4*(4064256*x^12+10838016*x^
11+27448848*x^10+74497416*x^9+113632819*x^8+161952882*x^7+202570211*x^6+187394037*x^5+155202669*x^
4+108718461*x^3+51847177*x^2+17383563*x+3537770)/(3*x+2)^2/(2*x+1)^2/(x+1)^2/(3*x^2-x+3)^2/(84*x^2
-35*x+106)^2,
Dx^2-1/4*(768*x^14-2688*x^12-7936*x^11-3408*x^10+2656*x^9+6048*x^8-2376*x^7-8064*x^6
-8256*x^5-3168*x^4-684*x^3+23*x^2-150*x-20)/x^2/(x-2)^2/(4*x^2+4*x+3)^2/(2*x+1)^2/(2*x^3-1)^2,
Dx^
2-1/36*(112*x^16-224*x^15-744*x^14+18480*x^13+11403*x^12-137310*x^11+59032*x^10+312328*x^9-436773*
x^8+192678*x^7-37770*x^6+59112*x^5-61540*x^4+26096*x^3-5328*x^2+640*x-80)/x^2/(x-1)^2/(x^2+2*x-2)^
2/(x-2)^2/(4*x^4+8*x^3-7*x^2-2*x+1)^2,
Dx^2+1/4*(233055468*x^8-76640877*x^7+302127851*x^6+
453833583*x^5+35908719*x^4-208253479*x^3-75292959*x^2-10437147*x+1058841)/(x-21)^2/(9*x+7)^2/(3*x+
1)^2/x^2/(x-1)^2/(27*x-7)^2,
Dx^2+1/72*(16513112*x^10-45863268*x^9+45055140*x^8-15662223*x^7-\
1571736*x^6+1494579*x^5+215382*x^4-69801*x^3-10668*x^2-535*x+18)/x^2/(4*x+1)^2/(x-1)^2/(11*x^2-8*x
-1)^2/(11*x-1)^2/(2*x-1)^2,
Dx^2-1/4*(28*x^12-168*x^11+252*x^10+280*x^9-1857*x^8+3900*x^7-4544*x^6
+3006*x^5-1275*x^4+606*x^3-372*x^2+144*x-16)/x^2/(x-1)^2/(x-2)^2/(2*x-1)^2/(x+1)^2/(3*x^2-3*x+2)^2
,
Dx^2-1/36*(567*x^12+107352*x^11-28402272*x^10-13842739968*x^9-1670328988160*x^8-63689592102912*x
^7-479079206387712*x^6-232462420859289600*x^5-28090064548159488000*x^4-1212286308446306304000*x^3-\
24791306457380290560000*x^2-319053738440392704000000*x-3697685177900728320000000)/x^2/(x-180)^2/(3
*x+160)^2/(x+72)^2/(x+90)^2/(3*x^2-44*x-4608)^2,
Dx^2-(72900*x^14-1953720*x^13+18364725*x^12-\
74137410*x^11+75724227*x^10+368719380*x^9-1367036432*x^8+1957260580*x^7-1454740158*x^6+411788440*x
^5-751379*x^4-376914*x^3-43465*x^2+380*x-18)/x^2/(x-9)^2/(9*x^2-24*x-1)^2/(x-1)^2/(5*x-1)^2/(9*x^2
-42*x+1)^2,
Dx^2-1/36*(734832*x^14+1469664*x^13+215784*x^12-45034704*x^11+24527691*x^10+120244662*
x^9-25357032*x^8-103876254*x^7-27191387*x^6+4681200*x^5-2494875*x^4-2180750*x^3-397200*x^2-26250*x
-3125)/x^2/(3*x+1)^2/(x+1)^2/(3*x-5)^2/(3*x+5)^2/(12*x^3-20*x^2+x+1)^2]:

ALinp := Dx^2+(1/4)*(x^4-44*x^3+1206*x^2-44*x+1)/((x^2-34*x+1)^2*x^2):