\[ \left (a x^2+1\right ) y''(x)+b x y'(x)+c y(x)=0 \] ✓ Mathematica : cpu = 0.0669474 (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 = 0.138 (sec), leaf count = 124
\[\left \{y \left (x \right ) = \left (c_{1} \LegendreP \left (\frac {-a +\sqrt {a^{2}+b^{2}+\left (-2 b -4 c \right ) a}}{2 a}, \frac {2 a -b}{2 a}, \sqrt {-a}\, x \right )+c_{2} \LegendreQ \left (\frac {-a +\sqrt {a^{2}+b^{2}+\left (-2 b -4 c \right ) a}}{2 a}, \frac {2 a -b}{2 a}, \sqrt {-a}\, x \right )\right ) \left (a \,x^{2}+1\right )^{\frac {2 a -b}{4 a}}\right \}\]