\[ y''(x)=-\frac {\left (a x^2+a-1\right ) y'(x)}{x \left (x^2+1\right )}-\frac {y(x) \left (b x^2+c\right )}{x^2 \left (x^2+1\right )} \] ✓ Mathematica : cpu = 0.78533 (sec), leaf count = 264
\[\left \{\left \{y(x)\to x^{-\frac {1}{2} \sqrt {a^2-4 a-4 c+4}-\frac {a}{2}+1} \left (c_1 \, _2F_1\left (\frac {1}{4} \left (-\sqrt {a^2-2 a-4 b+1}-\sqrt {a^2-4 a-4 c+4}+1\right ),\frac {1}{4} \left (\sqrt {a^2-2 a-4 b+1}-\sqrt {a^2-4 a-4 c+4}+1\right );1-\frac {1}{2} \sqrt {a^2-4 a-4 c+4};-x^2\right )+c_2 x^{\sqrt {a^2-4 a-4 c+4}} \, _2F_1\left (\frac {1}{4} \left (-\sqrt {a^2-2 a-4 b+1}+\sqrt {a^2-4 a-4 c+4}+1\right ),\frac {1}{4} \left (\sqrt {a^2-2 a-4 b+1}+\sqrt {a^2-4 a-4 c+4}+1\right );\frac {1}{2} \left (\sqrt {a^2-4 a-4 c+4}+2\right );-x^2\right )\right )\right \}\right \}\]
✓ Maple : cpu = 0.13 (sec), leaf count = 97
\[ \left \{ y \left ( x \right ) ={x}^{1-{\frac {a}{2}}} \left ( {\it LegendreQ} \left ( -{\frac {1}{2}}+{\frac {1}{2}\sqrt {{a}^{2}-2\,a-4\,b+1}},{\frac {1}{2}\sqrt {{a}^{2}-4\,a-4\,c+4}},\sqrt {{x}^{2}+1} \right ) {\it \_C2}+{\it LegendreP} \left ( -{\frac {1}{2}}+{\frac {1}{2}\sqrt {{a}^{2}-2\,a-4\,b+1}},{\frac {1}{2}\sqrt {{a}^{2}-4\,a-4\,c+4}},\sqrt {{x}^{2}+1} \right ) {\it \_C1} \right ) \right \} \]