ODE
\[ \text {a1} x \left (1-x^2\right ) y'(x)+y(x) \left (\text {a2}+\text {b2} x+\text {c2} x^2\right )+\left (1-x^2\right )^2 y''(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 39.5334 (sec), leaf count = 1
\[\text {$\$$Aborted}\]
Maple ✓
cpu = 0.688 (sec), leaf count = 441
\[\left [y \left (x \right ) = \textit {\_C1} \left (-\frac {1}{2}+\frac {x}{2}\right )^{\frac {1}{2}+\frac {\sqrt {\mathit {a1}^{2}+4 \mathit {a1} -4 \mathit {a2} -4 \mathit {b2} -4 \mathit {c2} +4}}{4}} \left (\frac {1}{2}+\frac {x}{2}\right )^{\frac {1}{2}-\frac {\sqrt {\mathit {a1}^{2}+4 \mathit {a1} -4 \mathit {a2} +4 \mathit {b2} -4 \mathit {c2} +4}}{4}} \left (x^{2}-1\right )^{\frac {\mathit {a1}}{4}} \hypergeom \left (\left [\frac {\sqrt {\mathit {a1}^{2}+4 \mathit {a1} -4 \mathit {a2} -4 \mathit {b2} -4 \mathit {c2} +4}}{4}+\frac {\sqrt {\mathit {a1}^{2}+2 \mathit {a1} -4 \mathit {c2} +1}}{2}-\frac {\sqrt {\mathit {a1}^{2}+4 \mathit {a1} -4 \mathit {a2} +4 \mathit {b2} -4 \mathit {c2} +4}}{4}+\frac {1}{2}, \frac {\sqrt {\mathit {a1}^{2}+4 \mathit {a1} -4 \mathit {a2} -4 \mathit {b2} -4 \mathit {c2} +4}}{4}-\frac {\sqrt {\mathit {a1}^{2}+2 \mathit {a1} -4 \mathit {c2} +1}}{2}-\frac {\sqrt {\mathit {a1}^{2}+4 \mathit {a1} -4 \mathit {a2} +4 \mathit {b2} -4 \mathit {c2} +4}}{4}+\frac {1}{2}\right ], \left [1-\frac {\sqrt {\mathit {a1}^{2}+4 \mathit {a1} -4 \mathit {a2} +4 \mathit {b2} -4 \mathit {c2} +4}}{2}\right ], \frac {1}{2}+\frac {x}{2}\right )+\textit {\_C2} \left (-\frac {1}{2}+\frac {x}{2}\right )^{\frac {1}{2}+\frac {\sqrt {\mathit {a1}^{2}+4 \mathit {a1} -4 \mathit {a2} -4 \mathit {b2} -4 \mathit {c2} +4}}{4}} \left (\frac {1}{2}+\frac {x}{2}\right )^{\frac {1}{2}+\frac {\sqrt {\mathit {a1}^{2}+4 \mathit {a1} -4 \mathit {a2} +4 \mathit {b2} -4 \mathit {c2} +4}}{4}} \left (x^{2}-1\right )^{\frac {\mathit {a1}}{4}} \hypergeom \left (\left [\frac {\sqrt {\mathit {a1}^{2}+4 \mathit {a1} -4 \mathit {a2} -4 \mathit {b2} -4 \mathit {c2} +4}}{4}+\frac {\sqrt {\mathit {a1}^{2}+2 \mathit {a1} -4 \mathit {c2} +1}}{2}+\frac {\sqrt {\mathit {a1}^{2}+4 \mathit {a1} -4 \mathit {a2} +4 \mathit {b2} -4 \mathit {c2} +4}}{4}+\frac {1}{2}, \frac {\sqrt {\mathit {a1}^{2}+4 \mathit {a1} -4 \mathit {a2} -4 \mathit {b2} -4 \mathit {c2} +4}}{4}-\frac {\sqrt {\mathit {a1}^{2}+2 \mathit {a1} -4 \mathit {c2} +1}}{2}+\frac {\sqrt {\mathit {a1}^{2}+4 \mathit {a1} -4 \mathit {a2} +4 \mathit {b2} -4 \mathit {c2} +4}}{4}+\frac {1}{2}\right ], \left [1+\frac {\sqrt {\mathit {a1}^{2}+4 \mathit {a1} -4 \mathit {a2} +4 \mathit {b2} -4 \mathit {c2} +4}}{2}\right ], \frac {1}{2}+\frac {x}{2}\right )\right ]\] Mathematica raw input
DSolve[(a2 + b2*x + c2*x^2)*y[x] + a1*x*(1 - x^2)*y'[x] + (1 - x^2)^2*y''[x] == 0,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve((-x^2+1)^2*diff(diff(y(x),x),x)+a1*x*(-x^2+1)*diff(y(x),x)+(c2*x^2+b2*x+a2)*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*(-1/2+1/2*x)^(1/2+1/4*(a1^2+4*a1-4*a2-4*b2-4*c2+4)^(1/2))*(1/2+1/2*x)^(1/2-1/4*(a1^2+4*a1-4*a2+4*b2-4*c2+4)^(1/2))*(x^2-1)^(1/4*a1)*hypergeom([1/4*(a1^2+4*a1-4*a2-4*b2-4*c2+4)^(1/2)+1/2*(a1^2+2*a1-4*c2+1)^(1/2)-1/4*(a1^2+4*a1-4*a2+4*b2-4*c2+4)^(1/2)+1/2, 1/4*(a1^2+4*a1-4*a2-4*b2-4*c2+4)^(1/2)-1/2*(a1^2+2*a1-4*c2+1)^(1/2)-1/4*(a1^2+4*a1-4*a2+4*b2-4*c2+4)^(1/2)+1/2],[1-1/2*(a1^2+4*a1-4*a2+4*b2-4*c2+4)^(1/2)],1/2+1/2*x)+_C2*(-1/2+1/2*x)^(1/2+1/4*(a1^2+4*a1-4*a2-4*b2-4*c2+4)^(1/2))*(1/2+1/2*x)^(1/2+1/4*(a1^2+4*a1-4*a2+4*b2-4*c2+4)^(1/2))*(x^2-1)^(1/4*a1)*hypergeom([1/4*(a1^2+4*a1-4*a2-4*b2-4*c2+4)^(1/2)+1/2*(a1^2+2*a1-4*c2+1)^(1/2)+1/4*(a1^2+4*a1-4*a2+4*b2-4*c2+4)^(1/2)+1/2, 1/4*(a1^2+4*a1-4*a2-4*b2-4*c2+4)^(1/2)-1/2*(a1^2+2*a1-4*c2+1)^(1/2)+1/4*(a1^2+4*a1-4*a2+4*b2-4*c2+4)^(1/2)+1/2],[1+1/2*(a1^2+4*a1-4*a2+4*b2-4*c2+4)^(1/2)],1/2+1/2*x)]