\[ y''(x)=-\frac {b x y'(x)}{a \left (x^2-1\right )}-\frac {y(x) \left (c x^2+d x+e\right )}{a \left (x^2-1\right )^2} \] ✓ Mathematica : cpu = 64.8077 (sec), leaf count = 1763961 \[ \text {Too large to display} \] ✓ Maple : cpu = 0.233 (sec), leaf count = 561
\[\left \{y \left (x \right ) = \left (c_{1} \left (\frac {x}{2}+\frac {1}{2}\right )^{\frac {2 a -\sqrt {4 a^{2}+b^{2}+\left (-4 b -4 c +4 d -4 e \right ) a}}{4 a}} \hypergeom \left (\left [\frac {2 a +\sqrt {4 a^{2}+b^{2}+\left (-4 b -4 c -4 d -4 e \right ) a}+2 \sqrt {a^{2}+b^{2}+\left (-2 b -4 c \right ) a}-\sqrt {4 a^{2}+b^{2}+\left (-4 b -4 c +4 d -4 e \right ) a}}{4 a}, \frac {2 a +\sqrt {4 a^{2}+b^{2}+\left (-4 b -4 c -4 d -4 e \right ) a}-2 \sqrt {a^{2}+b^{2}+\left (-2 b -4 c \right ) a}-\sqrt {4 a^{2}+b^{2}+\left (-4 b -4 c +4 d -4 e \right ) a}}{4 a}\right ], \left [-\frac {-2 a +\sqrt {4 a^{2}+b^{2}+\left (-4 b -4 c +4 d -4 e \right ) a}}{2 a}\right ], \frac {x}{2}+\frac {1}{2}\right )+c_{2} \left (\frac {x}{2}+\frac {1}{2}\right )^{\frac {2 a +\sqrt {4 a^{2}+b^{2}+\left (-4 b -4 c +4 d -4 e \right ) a}}{4 a}} \hypergeom \left (\left [\frac {2 a +\sqrt {4 a^{2}+b^{2}+\left (-4 b -4 c -4 d -4 e \right ) a}+2 \sqrt {a^{2}+b^{2}+\left (-2 b -4 c \right ) a}+\sqrt {4 a^{2}+b^{2}+\left (-4 b -4 c +4 d -4 e \right ) a}}{4 a}, \frac {2 a +\sqrt {4 a^{2}+b^{2}+\left (-4 b -4 c -4 d -4 e \right ) a}-2 \sqrt {a^{2}+b^{2}+\left (-2 b -4 c \right ) a}+\sqrt {4 a^{2}+b^{2}+\left (-4 b -4 c +4 d -4 e \right ) a}}{4 a}\right ], \left [\frac {2 a +\sqrt {4 a^{2}+b^{2}+\left (-4 b -4 c +4 d -4 e \right ) a}}{2 a}\right ], \frac {x}{2}+\frac {1}{2}\right )\right ) \left (\frac {x}{2}-\frac {1}{2}\right )^{\frac {2 a +\sqrt {4 a^{2}+b^{2}+\left (-4 b -4 c -4 d -4 e \right ) a}}{4 a}} \left (x^{2}-1\right )^{-\frac {b}{4 a}}\right \}\]