read "algo.maple_W17";

#  infolevel[dsolveBessel] := 10;
#  Uncomment the above line to see what the program is doing.

_Envdiffopdomain := [Dx,x];

dsolveBessel(x^2*Dx^2 + x*Dx - (x^2+(11/3)^2));

L := x*(x-1)^4*(x+1)^4*Dx^2+(x^2+1)*(x-1)^3*(x+1)^3*Dx-4*x^3*(v*x^2-v+1)*(v*x^2-v-1);
dsolveBessel(L);

L := 
Dx^2-3*(4*x^10-2*x^8+11*x^6-13*x^4-5*x^2+1)/x/(4*x^6-6*x^4-5*x^2+3)/(x^4+1)*Dx
+x^2*(12*x^18+18*x^16-83*x^14+83*x^12+534*x^10-714*x^8-299*x^6+315*x^4+224*x^2-58)
/(4*x^6-6*x^4-5*x^2+3)/(x^4+1)^4 ;
dsolveBessel(L);

L1 := Dx^2+(lambda^4*M^2*x^2+8*lambda^2*M*x^2+16*x^2-48*M)/x/(lambda^4*M^2*x^2
+8*lambda^2*M*x^2+16*x^2-16*M)*Dx+lambda^2*(-4*lambda^2*M^2-32*M+16*x^2+8*lambda^2*M*x^2
+lambda^4*M^2*x^2)/(lambda^4*M^2*x^2+8*lambda^2*M*x^2+16*x^2-16*M):
L2 := Dx^2+(lambda^4*M^2*x^2+8*lambda^2*M*x^2+16*x^2-48*M)/x/(lambda^4*M^2*x^2
+8*lambda^2*M*x^2+16*x^2-16*M)*Dx-(4*lambda^4*M^3+32*lambda^2*M^2+16*lambda^4*M^2*x^2
+128*x^2+80*lambda^2*M*x^2+x^2*lambda^6*M^3)/M/(lambda^4*M^2*x^2+8*lambda^2*M*x^2+16*x^2-16*M):

dsolveBessel(L1);
dsolveBessel(L2);

x^2*(x-1)^4*(x+1)^4*Dx^2+(2*x^9-6*x^7+6*x^5-2*x^3)*Dx+9/4*x^4+1/2*x^2-3/4*x^8+2*x^6;

dsolveBessel(%);

x*(x-1)^4*(x+1)^4*Dx^2+(x^2+1)*(x-1)^3*(x+1)^3*Dx-4*x^3*(1/4*x^2+3/4)*(1/4*x^2-5/4);
dsolveBessel(%);


L := Dx^2-2/(x-3)*Dx-1/4*(-9*x+10+x^2)/x/(x-3);
dsolveBessel(%);

eq1 :=
-(x^16+93*x^14+3450*x^12+62864*x^10+607200*x^8+3280896*x^6+10027008*x^4+
15482880*x^2+7962624)/(32*x^2+x^4+96)/(x^8+48*x^6+656*x^4+3072*x^2+4608)/(6+x^
2)/x^2*y(x)-(x^10-18*x^8-1104*x^6-11424*x^4-50688*x^2-82944)/(6+x^2)/(x^8+48*x
^6+656*x^4+3072*x^2+4608)/x*diff(y(x),x)+diff(diff(y(x),x),x);
de2diffop(eq1,y(x));
dsolveBessel(%);