\[ y''(x)=-\frac {\left (a x^2+a-2\right ) y'(x)}{x \left (x^2-1\right )}-\frac {b y(x)}{x^2} \] ✓ Mathematica : cpu = 0.89897 (sec), leaf count = 211
\[\left \{\left \{y(x)\to (-1)^{\frac {1}{4} \left (-\sqrt {a^2-2 a-4 b+1}+a+7\right )} x^{\frac {1}{2} \left (-\sqrt {a^2-2 a-4 b+1}+a-1\right )} \left (c_1 \, _2F_1\left (\frac {a-1}{2},\frac {1}{2} \left (a-\sqrt {a^2-2 a-4 b+1}-1\right );1-\frac {1}{2} \sqrt {a^2-2 a-4 b+1};x^2\right )+c_2 i^{\sqrt {a^2-2 a-4 b+1}} x^{\sqrt {a^2-2 a-4 b+1}} \, _2F_1\left (\frac {a-1}{2},\frac {1}{2} \left (a+\sqrt {a^2-2 a-4 b+1}-1\right );\frac {1}{2} \left (\sqrt {a^2-2 a-4 b+1}+2\right );x^2\right )\right )\right \}\right \}\]
✓ Maple : cpu = 0.148 (sec), leaf count = 161
\[ \left \{ y \left ( x \right ) = \left ( {x}^{2}-1 \right ) ^{-a+2} \left ( {x}^{{\frac {a}{2}}-{\frac {1}{2}}-{\frac {1}{2}\sqrt {{a}^{2}-2\,a-4\,b+1}}}{\mbox {$_2$F$_1$}(-{\frac {a}{2}}+{\frac {3}{2}},-{\frac {a}{2}}+{\frac {3}{2}}-{\frac {1}{2}\sqrt {{a}^{2}-2\,a-4\,b+1}};\,1-{\frac {1}{2}\sqrt {{a}^{2}-2\,a-4\,b+1}};\,{x}^{2})}{\it \_C2}+{x}^{{\frac {a}{2}}-{\frac {1}{2}}+{\frac {1}{2}\sqrt {{a}^{2}-2\,a-4\,b+1}}}{\mbox {$_2$F$_1$}(-{\frac {a}{2}}+{\frac {3}{2}},-{\frac {a}{2}}+{\frac {3}{2}}+{\frac {1}{2}\sqrt {{a}^{2}-2\,a-4\,b+1}};\,1+{\frac {1}{2}\sqrt {{a}^{2}-2\,a-4\,b+1}};\,{x}^{2})}{\it \_C1} \right ) \right \} \]