# 17 Equations
#
# hypergeometricsols finds hypergeometric solutions of all of the differential 
# operators in the list Linp below. 
#
# Then 
# type hypergeometricsols( Linp[i] ) where i=1,...,17.

Linp := [Dx^2+(28*x-5)/x/(4*x-1)*Dx+(144*x^2+20*x-3)/x^2/(4*x-1)/(1+4*x),
Dx^2+2*(112*
x^3-168*x^2+73*x-9)/x/(-1+2*x)/(16*x^2-16*x+3)*Dx+4*(576*x^5-1024*x^4+488*x^3-\
15*x^2-27*x+3)/(-1+2*x)^2/x^2/(1+4*x)/(16*x^2-16*x+3), Dx^2+4*(24*x^2-1)/x/(16
*x^2-1)*Dx+2*(192*x^3-56*x^2-6*x+1)/x^2/(4*x-1)/(16*x^2-1), Dx^2+2*(256*x^4+80
*x^3-111*x^2-14*x+2)/x/(64*x^4+40*x^3-30*x^2-5*x+1)*Dx+2*(384*x^4+4*x^3-153*x^
2-15*x+1)/x^2/(64*x^4+40*x^3-30*x^2-5*x+1), Dx^2+4*(1296*x^5+576*x^4-144*x^3-\
72*x^2+x+1)/x/(864*x^5+432*x^4-96*x^3-48*x^2+2*x+1)*Dx+2*(5184*x^6-864*x^5-\
1656*x^4+48*x^3+162*x^2+6*x-1)/(-1+2*x)/x^2/(864*x^5+432*x^4-96*x^3-48*x^2+2*x
+1), Dx^2+2*(3317760*x^13-1990656*x^12+1078272*x^11-138240*x^10-304128*x^9+
342144*x^8-139584*x^7+24096*x^6+336*x^5-7384*x^4+2112*x^3+202*x^2-99*x+7)/x/(
331776*x^12-82944*x^11+82944*x^10+6912*x^9-20736*x^8+19584*x^7-3648*x^6+864*x^
5+480*x^4-484*x^3+16*x^2+23*x-2)/(-1+2*x)*Dx+4/x^2*(6635520*x^14-6303744*x^13+
2985984*x^12-297216*x^11-1237248*x^10+1437696*x^9-764736*x^8+183648*x^7-14208*
x^6-22736*x^5+12796*x^4-1325*x^3-313*x^2+68*x-4)/(-1+2*x)^2/(331776*x^12-82944
*x^11+82944*x^10+6912*x^9-20736*x^8+19584*x^7-3648*x^6+864*x^5+480*x^4-484*x^3
+16*x^2+23*x-2), Dx^2+2*(2359296*x^14-1429504*x^13-559104*x^12+1264640*x^11-\
257536*x^10+229568*x^9-78880*x^8-70272*x^7+10128*x^6+2244*x^5-6*x^4+719*x^3-87
*x^2-45*x+7)/x/(-1+2*x)/(196608*x^13-4096*x^12-106496*x^11+90112*x^10+4096*x^9
+16192*x^8+3776*x^7-4736*x^6-560*x^5-124*x^4-33*x^3+52*x^2+7*x-2)*Dx+2*(
11796480*x^15-14049280*x^14+3866624*x^13+4591616*x^12-2048000*x^11+1149952*x^
10-776192*x^9-303232*x^8+176832*x^7+10272*x^6-8148*x^5+4874*x^4-1471*x^3-120*x
^2+82*x-8)/x^2/(-1+2*x)^2/(196608*x^13-4096*x^12-106496*x^11+90112*x^10+4096*x
^9+16192*x^8+3776*x^7-4736*x^6-560*x^5-124*x^4-33*x^3+52*x^2+7*x-2), Dx^2+2*(
13934592*x^14-20348928*x^13+18367488*x^12-4910592*x^11-3151104*x^10-350720*x^9
-909248*x^8+287232*x^7+18736*x^6+29728*x^5+5192*x^4-4914*x^3-72*x^2+144*x-9)/(
995328*x^13-2036736*x^12+2253312*x^11-1520640*x^10+491520*x^9-212992*x^8+9536*
x^7+21184*x^6-1888*x^5+2420*x^4-990*x^3-108*x^2+57*x-3)/(2*x+1)/x*Dx+2*(
83607552*x^15-73101312*x^14+58042368*x^13+34481664*x^12-27326208*x^11-12044160
*x^10-5819328*x^9-130336*x^8+475728*x^7+98808*x^6+114460*x^5+2016*x^4-8736*x^3
+126*x^2+39*x-6)/(2*x+1)^2/x^2/(995328*x^13-2036736*x^12+2253312*x^11-1520640*
x^10+491520*x^9-212992*x^8+9536*x^7+21184*x^6-1888*x^5+2420*x^4-990*x^3-108*x^
2+57*x-3), Dx^2+(2752512*x^12-2473984*x^11+1345536*x^10+497216*x^9-2492736*x^8
+997104*x^7-136176*x^6+56533*x^5-3285*x^4-2741*x^3-27*x^2-228*x+60)/(172032*x^
12-155648*x^11+20480*x^10+78016*x^9-188224*x^8+78144*x^7-6528*x^6+701*x^5+2131
*x^4-1183*x^3+97*x^2-30*x+12)/x*Dx+3*(3211264*x^11-2867200*x^10+2651136*x^9-\
184320*x^8-2234432*x^7+855680*x^6-138208*x^5+77193*x^4-20140*x^3+4187*x^2-728*
x-100)/(172032*x^12-155648*x^11+20480*x^10+78016*x^9-188224*x^8+78144*x^7-6528
*x^6+701*x^5+2131*x^4-1183*x^3+97*x^2-30*x+12)/x, Dx^2+2*(264241152*x^16+
1340866560*x^15+2740060160*x^14+3349266432*x^13+3068207104*x^12+2384950272*x^
11+1540036096*x^10+748700416*x^9+247670976*x^8+47599408*x^7+1891360*x^6-\
1501848*x^5-387788*x^4-35369*x^3+904*x^2+445*x+27)/(6291456*x^15+31195136*x^14
+62308352*x^13+72646656*x^12+61540352*x^11+43743232*x^10+25947904*x^9+11327232
*x^8+3013920*x^7+237056*x^6-124720*x^5-43192*x^4-4058*x^3+446*x^2+124*x+9)/(6*
x+1)/x*Dx+2*(9512681472*x^18+54131687424*x^17+127609995264*x^16+182913073152*x
^15+195411658752*x^14+174538459136*x^13+131529485056*x^12+79157857280*x^11+
36000494528*x^10+11859309184*x^9+2681073584*x^8+359992976*x^7+7834972*x^6-\
7606456*x^5-1651438*x^4-162815*x^3-6100*x^2+207*x+18)/(6291456*x^15+31195136*x
^14+62308352*x^13+72646656*x^12+61540352*x^11+43743232*x^10+25947904*x^9+
11327232*x^8+3013920*x^7+237056*x^6-124720*x^5-43192*x^4-4058*x^3+446*x^2+124*
x+9)/(2*x+1)/x^2/(6*x+1)^2, Dx^2+(134479872*x^15+165298176*x^14-350183424*x^13
-1144667136*x^12-1501585920*x^11-1203699456*x^10-643005248*x^9-228680400*x^8-\
49303712*x^7-3613256*x^6+1231204*x^5+413695*x^4+46788*x^3-452*x^2-606*x-42)/(
1400832*x^14+1867776*x^13-3136512*x^12-10636288*x^11-13416576*x^10-10023296*x^
9-4785648*x^8-1383488*x^7-160312*x^6+39660*x^5+19091*x^4+2611*x^3-94*x^2-65*x-\
6)/x/(6*x+1)*Dx+6*(941359104*x^17+1529708544*x^16-2282517504*x^15-10326950912*
x^14-16544871296*x^13-16293818624*x^12-11086860128*x^11-5406390304*x^10-\
1889367800*x^9-455634752*x^8-66160902*x^7-1895366*x^6+1462247*x^5+332096*x^4+
30698*x^3+406*x^2-144*x-8)/(1400832*x^14+1867776*x^13-3136512*x^12-10636288*x^
11-13416576*x^10-10023296*x^9-4785648*x^8-1383488*x^7-160312*x^6+39660*x^5+
19091*x^4+2611*x^3-94*x^2-65*x-6)/(2*x+1)/x^2/(6*x+1)^2, Dx^2+2*(45342720*x^16
+144290304*x^15+189849600*x^14+107521792*x^13-39371136*x^12-122365888*x^11-\
110536928*x^10-60124192*x^9-20522600*x^8-3802342*x^7+93358*x^6+221351*x^5+
50642*x^4+4202*x^3-300*x^2-75*x-12)/(5667840*x^16+20109312*x^15+28356864*x^14+
17725952*x^13-2727808*x^12-14903680*x^11-13628128*x^10-7143840*x^9-2200052*x^8
-271904*x^7+83757*x^6+43688*x^5+7231*x^4-16*x^3-213*x^2-24*x-3)/x*Dx+2*(
158699520*x^16+446971392*x^15+548752896*x^14+264480512*x^13-189427328*x^12-\
426516160*x^11-378629728*x^10-210953856*x^9-77609064*x^8-17511490*x^7-1417288*
x^6+305365*x^5+113624*x^4+16254*x^3+1002*x^2-57*x-18)/x^2/(5667840*x^16+
20109312*x^15+28356864*x^14+17725952*x^13-2727808*x^12-14903680*x^11-13628128*
x^10-7143840*x^9-2200052*x^8-271904*x^7+83757*x^6+43688*x^5+7231*x^4-16*x^3-\
213*x^2-24*x-3), Dx^2+(260997120*x^18+663450624*x^17+750855168*x^16+641317120*
x^15+315141888*x^14-163456576*x^13-430571712*x^12-407475264*x^11-235774592*x^
10-92318888*x^9-28796712*x^8-5101087*x^7+184329*x^6+300249*x^5+67833*x^4+6163*
x^3+27*x^2-69*x-21)/(16312320*x^18+45167616*x^17+45732864*x^16+24396544*x^15-\
1517504*x^14-30982592*x^13-42343824*x^12-32941040*x^11-16946844*x^10-5575272*x
^9-1319911*x^8-96520*x^7+77896*x^6+31496*x^5+5138*x^4-216*x^3-132*x^2-16*x-3)/
x*Dx+(913489920*x^18+2114767872*x^17+2673100800*x^16+2819058944*x^15+
1971984256*x^14+484145344*x^13-586510336*x^12-878329536*x^11-604607192*x^10-\
291482456*x^9-112118224*x^8-26354577*x^7-2531790*x^6+241305*x^5+125748*x^4+
25913*x^3+2634*x^2+39*x-24)/x^2/(16312320*x^18+45167616*x^17+45732864*x^16+
24396544*x^15-1517504*x^14-30982592*x^13-42343824*x^12-32941040*x^11-16946844*
x^10-5575272*x^9-1319911*x^8-96520*x^7+77896*x^6+31496*x^5+5138*x^4-216*x^3-\
132*x^2-16*x-3), Dx^2+(47059107840*x^23+224676384768*x^22-135584824320*x^21-\
330894389952*x^20-20012240448*x^19+15956332272*x^18+93077602752*x^17+
123328510917*x^16+5030417535*x^15-35246211975*x^14-16174999155*x^13+213773450*
x^12+4017901172*x^11+1073608080*x^10-404286016*x^9-164561907*x^8+16032943*x^7+
10643097*x^6+30621*x^5-331096*x^4-14978*x^3+5134*x^2+182*x-36)/(2941194240*x^
22+10171256832*x^21-17901720576*x^20+1598920128*x^19-5208329088*x^18-\
3077716896*x^17+12401046096*x^16+3559925085*x^15-3316551675*x^14-1578147513*x^
13+35012711*x^12+321803908*x^11+100231872*x^10-33116504*x^9-16553312*x^8+
1610821*x^7+1195205*x^6-17297*x^5-43569*x^4-1286*x^3+790*x^2+34*x-6)/(x+1)/x*
Dx+(164706877440*x^24+1003144310784*x^23+317537252352*x^22-1923840764928*x^21-\
1404463352832*x^20+335325048192*x^19+608646548592*x^18+424006643835*x^17+
154495759836*x^16-73760873016*x^15-80065079184*x^14-28876093715*x^13+
3766535544*x^12+9176559844*x^11+1925572904*x^10-875434413*x^9-317223628*x^8+
21620200*x^7+18513696*x^6+974719*x^5-420624*x^4-38004*x^3+4152*x^2+102*x-24)/(
x+1)^2/x^2/(2941194240*x^22+10171256832*x^21-17901720576*x^20+1598920128*x^19-\
5208329088*x^18-3077716896*x^17+12401046096*x^16+3559925085*x^15-3316551675*x^
14-1578147513*x^13+35012711*x^12+321803908*x^11+100231872*x^10-33116504*x^9-\
16553312*x^8+1610821*x^7+1195205*x^6-17297*x^5-43569*x^4-1286*x^3+790*x^2+34*x
-6), Dx^2+(30277632000*x^22+147569049600*x^21-367518105600*x^20-984374222848*x
^19-462073917440*x^18+700928313344*x^17+1101335099392*x^16+473644423168*x^15-\
159825694720*x^14-250851077120*x^13-113737409472*x^12-31492093728*x^11-\
10645868880*x^10-5122133080*x^9-1827140072*x^8-343696396*x^7-8304628*x^6+
9373288*x^5+1547096*x^4+29379*x^3-10812*x^2-509*x+18)/(1892352000*x^22+
9122611200*x^21-18640527360*x^20-58034765824*x^19-38532706304*x^18+41965621248
*x^17+94071750144*x^16+56013030400*x^15-5294450432*x^14-21996570880*x^13-\
10952369952*x^12-2543280896*x^11-537441232*x^10-276140992*x^9-112877022*x^8-\
19917936*x^7+1121240*x^6+1056920*x^5+134035*x^4-5391*x^3-2254*x^2-103*x+3)/x*
Dx+(105971712000*x^22+522117120000*x^21-1532547809280*x^20-3565570211840*x^19-\
937287933952*x^18+2615040987136*x^17+2671998829568*x^16+528180972544*x^15-\
722004656128*x^14-610977784064*x^13-233610538048*x^12-73660818368*x^11-\
35553068512*x^10-18158926064*x^9-6252763108*x^8-1236595460*x^7-95092852*x^6+
10870504*x^5+2870648*x^4+188941*x^3+1700*x^2+33*x+12)/x^2/(1892352000*x^22+
9122611200*x^21-18640527360*x^20-58034765824*x^19-38532706304*x^18+41965621248
*x^17+94071750144*x^16+56013030400*x^15-5294450432*x^14-21996570880*x^13-\
10952369952*x^12-2543280896*x^11-537441232*x^10-276140992*x^9-112877022*x^8-\
19917936*x^7+1121240*x^6+1056920*x^5+134035*x^4-5391*x^3-2254*x^2-103*x+3), Dx
^2+(135683112960*x^22-216400232448*x^21-881591869440*x^20-743472465408*x^19-\
408851804160*x^18-118557145344*x^17+147806728320*x^16+98030953992*x^15+
4050448256*x^14-15410867842*x^13-6408609508*x^12+1850671727*x^11+1431433844*x^
10-204312211*x^9-188968530*x^8+6346158*x^7+13207768*x^6+666376*x^5-397800*x^4-\
37557*x^3+4356*x^2+381*x-18)/(8480194560*x^22-10534551552*x^21-50391908352*x^
20-50341446144*x^19-45028601856*x^18-23078165376*x^17+15152198016*x^16+
14141918376*x^15+406236968*x^14-2356214710*x^13-725447438*x^12+214114051*x^11+
155870421*x^10-15954357*x^9-19631947*x^8+572822*x^7+1454362*x^6+41248*x^5-\
54948*x^4-3777*x^3+873*x^2+75*x-3)/x*Dx+(474890895360*x^22-924866740224*x^21-\
3309825908736*x^20-2188812386304*x^19-542721328128*x^18+153227486208*x^17+
328599749760*x^16+88571957976*x^15-23673542288*x^14-23381491646*x^13-\
4629125384*x^12+5913852913*x^11+2160018918*x^10-748212177*x^9-360040036*x^8+
17730722*x^7+23283620*x^6+2024336*x^5-407160*x^4-63195*x^3+150*x^2+15*x-12)/x^
2/(8480194560*x^22-10534551552*x^21-50391908352*x^20-50341446144*x^19-\
45028601856*x^18-23078165376*x^17+15152198016*x^16+14141918376*x^15+406236968*
x^14-2356214710*x^13-725447438*x^12+214114051*x^11+155870421*x^10-15954357*x^9
-19631947*x^8+572822*x^7+1454362*x^6+41248*x^5-54948*x^4-3777*x^3+873*x^2+75*x
-3), Dx^2+(57659392000*x^23-479040486400*x^22-115473331200*x^21+1654743178752*
x^20+660832360960*x^19-1827562189184*x^18-1971374645120*x^17+336623019328*x^16
+1714365443776*x^15+847296860532*x^14-261508818260*x^13-421440201210*x^12-\
167007671758*x^11-15242534376*x^10+11734205852*x^9+5329675769*x^8+880157807*x^
7-11482585*x^6-25934197*x^5-2952066*x^4+75660*x^3+27550*x^2+260*x-90)/(
1801856000*x^22-14993382400*x^21+3836856320*x^20+43648062208*x^19+6154083840*x
^18-50989450944*x^17-54577076576*x^16+27002115888*x^15+58752540732*x^14+
11074917368*x^13-18744006450*x^12-11943827034*x^11-2005747424*x^10+584373384*x
^9+346479237*x^8+58247942*x^7-3206910*x^6-2603142*x^5-259585*x^4+22663*x^3+
4831*x^2+67*x-15)/x/(2*x+1)*Dx+(403615744000*x^24-3348049152000*x^23-\
2614085365760*x^22+12537217740800*x^21+9790758756352*x^20-12966166104832*x^19-\
18023481409536*x^18-1287396053248*x^17+11117230185984*x^16+8333293263448*x^15+
743999622576*x^14-2323935615824*x^13-1568396323256*x^12-416402279570*x^11+
16036336456*x^10+50967909630*x^9+18119641396*x^8+3005787561*x^7+126147460*x^6-\
38660625*x^5-6328112*x^4-244878*x^3+10060*x^2+30*x-60)/(2*x+1)^2/x^2/(
1801856000*x^22-14993382400*x^21+3836856320*x^20+43648062208*x^19+6154083840*x
^18-50989450944*x^17-54577076576*x^16+27002115888*x^15+58752540732*x^14+
11074917368*x^13-18744006450*x^12-11943827034*x^11-2005747424*x^10+584373384*x
^9+346479237*x^8+58247942*x^7-3206910*x^6-2603142*x^5-259585*x^4+22663*x^3+
4831*x^2+67*x-15)]: