\[ x y'(x) \left ((2 a-1) \text {C0}+4 b^2 \text {B0} c^2 x^{2 c}\right )+(6-4 a) x^3 y^{(3)}(x)+x^2 y''(x) \left (\text {A0}+4 b^2 c^2 x^{2 c}\right )+y(x) \left (4 b^2 c^2 \text {D0} x^{2 c}+\text {E0}\right )+x^4 y^{(4)}(x)=0 \] ✗ Mathematica : cpu = 300.85 (sec), leaf count = 0
DSolve[(E0 + 4*b^2*c^2*D0*x^(2*c))*y[x] + x*((-1 + 2*a)*C0 + 4*b^2*B0*c^2*x^(2*c))*Derivative[1][y][x] + x^2*(A0 + 4*b^2*c^2*x^(2*c))*Derivative[2][y][x] + (6 - 4*a)*x^3*Derivative[3][y][x] + x^4*Derivative[4][y][x] == 0,y[x],x]
, timed out
$Aborted
✓ Maple : cpu = 0.363 (sec), leaf count = 63
dsolve(x^4*diff(diff(diff(diff(y(x),x),x),x),x)+(6-4*a)*x^3*diff(diff(diff(y(x),x),x),x)+(4*b^2*c^2*x^(2*c)+6*(a-1)^2-2*c^2*(mu^2+nu^2)+1)*x^2*diff(diff(y(x),x),x)+(4*(3*c-2*a+1)*b^2*c^2*x^(2*c)+(2*a-1)*(2*c^2*(mu^2+nu^2)-2*a*(a-1)-1))*x*diff(y(x),x)+(4*(a-c)*(a-2*c)*b^2*c^2*x^(2*c)+(c*mu+c*nu+a)*(c*mu+c*nu-a)*(c*mu-c*nu+a)*(c*mu-c*nu-a))*y(x)=0,y(x))
\[y \left (x \right ) = x^{a} \left (\left (\BesselJ \left (\mu , b \,x^{c}\right ) c_{2}+\BesselY \left (\mu , b \,x^{c}\right ) c_{3}\right ) \BesselJ \left (\nu , b \,x^{c}\right )+\BesselY \left (\nu , b \,x^{c}\right ) \left (c_{4} \BesselY \left (\mu , b \,x^{c}\right )+\BesselJ \left (\mu , b \,x^{c}\right ) c_{1}\right )\right )\]