\[ \boxed { \left ( a{x}^{2}+1 \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +bx{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +cy \left ( x \right ) =0} \]
Mathematica: cpu = 0.079510 (sec), leaf count = 162 \[ \left \{\left \{y(x)\to c_1 \left (a x^2+1\right )^{\frac {2 a-b}{4 a}} P_{\frac {\sqrt {a^2-2 b a-4 c a+b^2}-a}{2 a}}^{\frac {b-2 a}{2 a}}\left (i \sqrt {a} x\right )+c_2 \left (a x^2+1\right )^{\frac {2 a-b}{4 a}} Q_{\frac {\sqrt {a^2-2 b a-4 c a+b^2}-a}{2 a}}^{\frac {b-2 a}{2 a}}\left (i \sqrt {a} x\right )\right \}\right \} \]
Maple: cpu = 0.078 (sec), leaf count = 143 \[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( a{x}^{2}+1 \right ) ^{ {\frac {2\,a-b}{4\,a}}}{\it LegendreP} \left ( {\frac {1}{2\,a} \left ( \sqrt {{a}^{2}+ \left ( -2\,b-4\,c \right ) a+{b}^{2}}-a \right ) },{ \frac {2\,a-b}{2\,a}},\sqrt {-a}x \right ) +{\it \_C2}\, \left ( a{x}^{2 }+1 \right ) ^{{\frac {2\,a-b}{4\,a}}}{\it LegendreQ} \left ( {\frac {1 }{2\,a} \left ( \sqrt {{a}^{2}+ \left ( -2\,b-4\,c \right ) a+{b}^{2}}-a \right ) },{\frac {2\,a-b}{2\,a}},\sqrt {-a}x \right ) \right \} \]