\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) =-{\frac { \left ( a{x}^{2}+a-2 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{x \left ( {x}^{2}-1 \right ) }}-{\frac {by \left ( x \right ) }{{x}^{2}}}=0} \]
Mathematica: cpu = 0.803102 (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 = 0.109 (sec), leaf count = 171 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{x}^{{\frac {a}{2}}-{\frac {1 }{2}}+{\frac {1}{2}\sqrt {{a}^{2}-2\,a-4\,b+1}}} \left ( {x}^{2}-1 \right ) ^{-a+2} {\mbox {$_2$F$_1$}(-{\frac {a}{2}}+{\frac {3}{2}},-{\frac {a}{2}}+{\frac {3}{2}}+{\frac {1}{2}\sqrt {{a}^{2}-2\,a-4\,b+1}};\,1+{\frac {1}{2}\sqrt {{a}^{2}-2\,a-4\,b+1}};\,{x}^{2})} +{\it \_C2}\,{x}^{{\frac {a}{2}}-{\frac {1}{2}}-{\frac {1}{2}\sqrt {{a }^{2}-2\,a-4\,b+1}}} \left ( {x}^{2}-1 \right ) ^{-a+2} {\mbox {$_2$F$_1$}(-{\frac {a}{2}}+{\frac {3}{2}},-{\frac {a}{2}}+{\frac {3}{2}}-{\frac {1}{2}\sqrt {{a}^{2}-2\,a-4\,b+1}};\,1-{\frac {1}{2}\sqrt {{a}^{2}-2\,a-4\,b+1}};\,{x}^{2})} \right \} \]