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 = 57.2602 (sec), leaf count = 1
\[\text {$\$$Aborted}\]
Maple ✓
cpu = 0.165 (sec), leaf count = 404
\[ \left \{ y \left ( x \right ) = \left ( {x}^{2}-1 \right ) ^{{\frac {{\it a1}}{4}}} \left ( -{\frac {1}{2}}+{\frac {x}{2}} \right ) ^{{\frac {1}{2}}+{\frac {1}{4}\sqrt {{{\it a1}}^{2}+4\,{\it a1}-4\,{\it a2}-4\,{\it b2}-4\,{\it c2}+4}}} \left ( \left ( {\frac {1}{2}}+{\frac {x}{2}} \right ) ^{{\frac {1}{2}}+{\frac {1}{4}\sqrt {{{\it a1}}^{2}+4\,{\it a1}-4\,{\it a2}+4\,{\it b2}-4\,{\it c2}+4}}}{\mbox {$_2$F$_1$}({\frac {1}{4}\sqrt {{{\it a1}}^{2}+4\,{\it a1}-4\,{\it a2}-4\,{\it b2}-4\,{\it c2}+4}}+{\frac {1}{2}\sqrt {{{\it a1}}^{2}+2\,{\it a1}-4\,{\it c2}+1}}+{\frac {1}{4}\sqrt {{{\it a1}}^{2}+4\,{\it a1}-4\,{\it a2}+4\,{\it b2}-4\,{\it c2}+4}}+{\frac {1}{2}},{\frac {1}{4}\sqrt {{{\it a1}}^{2}+4\,{\it a1}-4\,{\it a2}-4\,{\it b2}-4\,{\it c2}+4}}-{\frac {1}{2}\sqrt {{{\it a1}}^{2}+2\,{\it a1}-4\,{\it c2}+1}}+{\frac {1}{4}\sqrt {{{\it a1}}^{2}+4\,{\it a1}-4\,{\it a2}+4\,{\it b2}-4\,{\it c2}+4}}+{\frac {1}{2}};\,1+{\frac {1}{2}\sqrt {{{\it a1}}^{2}+4\,{\it a1}-4\,{\it a2}+4\,{\it b2}-4\,{\it c2}+4}};\,{\frac {1}{2}}+{\frac {x}{2}})}{\it \_C2}+ \left ( {\frac {1}{2}}+{\frac {x}{2}} \right ) ^{{\frac {1}{2}}-{\frac {1}{4}\sqrt {{{\it a1}}^{2}+4\,{\it a1}-4\,{\it a2}+4\,{\it b2}-4\,{\it c2}+4}}}{\mbox {$_2$F$_1$}({\frac {1}{4}\sqrt {{{\it a1}}^{2}+4\,{\it a1}-4\,{\it a2}-4\,{\it b2}-4\,{\it c2}+4}}-{\frac {1}{2}\sqrt {{{\it a1}}^{2}+2\,{\it a1}-4\,{\it c2}+1}}-{\frac {1}{4}\sqrt {{{\it a1}}^{2}+4\,{\it a1}-4\,{\it a2}+4\,{\it b2}-4\,{\it c2}+4}}+{\frac {1}{2}},{\frac {1}{4}\sqrt {{{\it a1}}^{2}+4\,{\it a1}-4\,{\it a2}-4\,{\it b2}-4\,{\it c2}+4}}+{\frac {1}{2}\sqrt {{{\it a1}}^{2}+2\,{\it a1}-4\,{\it c2}+1}}-{\frac {1}{4}\sqrt {{{\it a1}}^{2}+4\,{\it a1}-4\,{\it a2}+4\,{\it b2}-4\,{\it c2}+4}}+{\frac {1}{2}};\,1-{\frac {1}{2}\sqrt {{{\it a1}}^{2}+4\,{\it a1}-4\,{\it a2}+4\,{\it b2}-4\,{\it c2}+4}};\,{\frac {1}{2}}+{\frac {x}{2}})}{\it \_C1} \right ) \right \} \] 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),'implicit')
Maple raw output
y(x) = (x^2-1)^(1/4*a1)*(-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))*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))*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)*_C1)