\[ y''(x)=-\frac {\left (a x^2+a-2\right ) y'(x)}{x \left (x^2-1\right )}-\frac {b y(x)}{x^2} \] ✓ Mathematica : cpu = 0.574665 (sec), leaf count = 236
\[\left \{\left \{y(x)\to c_1 (-1)^{\frac {1}{4} \left (-\sqrt {a^2-2 a-4 b+1}+a-1\right )} x^{\frac {1}{2} \left (-\sqrt {a^2-2 a-4 b+1}+a-1\right )} \, _2F_1\left (\frac {a}{2}-\frac {1}{2},\frac {a}{2}-\frac {1}{2} \sqrt {a^2-2 a-4 b+1}-\frac {1}{2};1-\frac {1}{2} \sqrt {a^2-2 a-4 b+1};x^2\right )+c_2 (-1)^{\frac {1}{4} \left (\sqrt {a^2-2 a-4 b+1}+a-1\right )} x^{\frac {1}{2} \left (\sqrt {a^2-2 a-4 b+1}+a-1\right )} \, _2F_1\left (\frac {a}{2}-\frac {1}{2},\frac {a}{2}+\frac {1}{2} \sqrt {a^2-2 a-4 b+1}-\frac {1}{2};\frac {1}{2} \sqrt {a^2-2 a-4 b+1}+1;x^2\right )\right \}\right \}\] ✓ Maple : cpu = 0.565 (sec), leaf count = 161
\[ \left \{ y \left ( x \right ) = \left ( {x}^{2}-1 \right ) ^{-a+2} \left ( {x}^{{\frac {a}{2}}-{\frac {1}{2}}-{\frac {1}{2}\sqrt {{a}^{2}-2\,a-4\,b+1}}}{\mbox {$_2$F$_1$}(-{\frac {a}{2}}+{\frac {3}{2}},-{\frac {a}{2}}+{\frac {3}{2}}-{\frac {1}{2}\sqrt {{a}^{2}-2\,a-4\,b+1}};\,1-{\frac {1}{2}\sqrt {{a}^{2}-2\,a-4\,b+1}};\,{x}^{2})}{\it \_C2}+{x}^{{\frac {a}{2}}-{\frac {1}{2}}+{\frac {1}{2}\sqrt {{a}^{2}-2\,a-4\,b+1}}}{\mbox {$_2$F$_1$}(-{\frac {a}{2}}+{\frac {3}{2}},-{\frac {a}{2}}+{\frac {3}{2}}+{\frac {1}{2}\sqrt {{a}^{2}-2\,a-4\,b+1}};\,1+{\frac {1}{2}\sqrt {{a}^{2}-2\,a-4\,b+1}};\,{x}^{2})}{\it \_C1} \right ) \right \} \]