\[ y''(x)=-\frac {b x y'(x)}{a \left (x^2-1\right )}-\frac {y(x) \left (c x^2+d x+e\right )}{a \left (x^2-1\right )^2} \] ✓ Mathematica : cpu = 69.3544 (sec), leaf count = 1763961 \[ \text {Too large to display} \] ✓ Maple : cpu = 0.672 (sec), leaf count = 561
\[ \left \{ y \left ( x \right ) = \left ( {x}^{2}-1 \right ) ^{-{\frac {b}{4\,a}}} \left ( -{\frac {1}{2}}+{\frac {x}{2}} \right ) ^{{\frac {1}{4\,a} \left ( 2\,a+\sqrt {4\,{a}^{2}+ \left ( -4\,b-4\,c-4\,d-4\,e \right ) a+{b}^{2}} \right ) }} \left ( {\mbox {$_2$F$_1$}(-{\frac {1}{4\,a} \left ( -\sqrt {4\,{a}^{2}+ \left ( -4\,b-4\,c-4\,d-4\,e \right ) a+{b}^{2}}+2\,\sqrt {{a}^{2}+ \left ( -2\,b-4\,c \right ) a+{b}^{2}}+\sqrt {4\,{a}^{2}+ \left ( -4\,b-4\,c+4\,d-4\,e \right ) a+{b}^{2}}-2\,a \right ) },-{\frac {1}{4\,a} \left ( -\sqrt {4\,{a}^{2}+ \left ( -4\,b-4\,c-4\,d-4\,e \right ) a+{b}^{2}}-2\,\sqrt {{a}^{2}+ \left ( -2\,b-4\,c \right ) a+{b}^{2}}+\sqrt {4\,{a}^{2}+ \left ( -4\,b-4\,c+4\,d-4\,e \right ) a+{b}^{2}}-2\,a \right ) };\,-{\frac {1}{2\,a} \left ( -2\,a+\sqrt {4\,{a}^{2}+ \left ( -4\,b-4\,c+4\,d-4\,e \right ) a+{b}^{2}} \right ) };\,{\frac {1}{2}}+{\frac {x}{2}})} \left ( {\frac {1}{2}}+{\frac {x}{2}} \right ) ^{{\frac {1}{4\,a} \left ( 2\,a-\sqrt {4\,{a}^{2}+ \left ( -4\,b-4\,c+4\,d-4\,e \right ) a+{b}^{2}} \right ) }}{\it \_C1}+{\mbox {$_2$F$_1$}({\frac {1}{4\,a} \left ( \sqrt {4\,{a}^{2}+ \left ( -4\,b-4\,c-4\,d-4\,e \right ) a+{b}^{2}}-2\,\sqrt {{a}^{2}+ \left ( -2\,b-4\,c \right ) a+{b}^{2}}+\sqrt {4\,{a}^{2}+ \left ( -4\,b-4\,c+4\,d-4\,e \right ) a+{b}^{2}}+2\,a \right ) },{\frac {1}{4\,a} \left ( \sqrt {4\,{a}^{2}+ \left ( -4\,b-4\,c-4\,d-4\,e \right ) a+{b}^{2}}+2\,\sqrt {{a}^{2}+ \left ( -2\,b-4\,c \right ) a+{b}^{2}}+\sqrt {4\,{a}^{2}+ \left ( -4\,b-4\,c+4\,d-4\,e \right ) a+{b}^{2}}+2\,a \right ) };\,{\frac {1}{2\,a} \left ( 2\,a+\sqrt {4\,{a}^{2}+ \left ( -4\,b-4\,c+4\,d-4\,e \right ) a+{b}^{2}} \right ) };\,{\frac {1}{2}}+{\frac {x}{2}})} \left ( {\frac {1}{2}}+{\frac {x}{2}} \right ) ^{{\frac {1}{4\,a} \left ( 2\,a+\sqrt {4\,{a}^{2}+ \left ( -4\,b-4\,c+4\,d-4\,e \right ) a+{b}^{2}} \right ) }}{\it \_C2} \right ) \right \} \]