\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) =-{\frac {ax{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{{x}^{2}+1}}-{\frac {by \left ( x \right ) }{ \left ( {x}^{2}+1 \right ) ^{2}}}=0} \]
Mathematica: cpu = 0.026503 (sec), leaf count = 106 \[ \left \{\left \{y(x)\to c_1 \left (x^2+1\right )^{\frac {2-a}{4}} P_{\frac {a-2}{2}}^{\frac {1}{2} \sqrt {a^2-4 a+4 b+4}}(i x)+c_2 \left (x^2+1\right )^{\frac {2-a}{4}} Q_{\frac {a-2}{2}}^{\frac {1}{2} \sqrt {a^2-4 a+4 b+4}}(i x)\right \}\right \} \]
Maple: cpu = 0.062 (sec), leaf count = 81 \[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( {x}^{2}+1 \right ) ^{{ \frac {1}{2}}-{\frac {a}{4}}}{\it LegendreP} \left ( {\frac {a}{2}}-1,{ \frac {1}{2}\sqrt {{a}^{2}-4\,a+4\,b+4}},ix \right ) +{\it \_C2}\, \left ( {x}^{2}+1 \right ) ^{{\frac {1}{2}}-{\frac {a}{4}}}{\it LegendreQ} \left ( {\frac {a}{2}}-1,{\frac {1}{2}\sqrt {{a}^{2}-4\,a+4 \,b+4}},ix \right ) \right \} \]