\[ a x y'(x)+y(x) \left (b x^m+c\right )+x^2 y''(x)=0 \] ✓ Mathematica : cpu = 0.0581232 (sec), leaf count = 445
\[\left \{\left \{y(x)\to c_1 m^{-\frac {-\sqrt {a^2-2 a-4 c+1}-a+1}{m}-\frac {\sqrt {a^2-2 a-4 c+1}}{m}} b^{\frac {-\sqrt {a^2-2 a-4 c+1}-a+1}{2 m}+\frac {\sqrt {a^2-2 a-4 c+1}}{2 m}} \left (x^m\right )^{\frac {-\sqrt {a^2-2 a-4 c+1}-a+1}{2 m}+\frac {\sqrt {a^2-2 a-4 c+1}}{2 m}} \Gamma \left (1-\frac {\sqrt {a^2-2 a-4 c+1}}{m}\right ) J_{-\frac {\sqrt {a^2-2 a-4 c+1}}{m}}\left (\frac {2 \sqrt {b} \sqrt {x^m}}{m}\right )+c_2 m^{\frac {\sqrt {a^2-2 a-4 c+1}}{m}-\frac {\sqrt {a^2-2 a-4 c+1}-a+1}{m}} b^{\frac {\sqrt {a^2-2 a-4 c+1}-a+1}{2 m}-\frac {\sqrt {a^2-2 a-4 c+1}}{2 m}} \left (x^m\right )^{\frac {\sqrt {a^2-2 a-4 c+1}-a+1}{2 m}-\frac {\sqrt {a^2-2 a-4 c+1}}{2 m}} \Gamma \left (\frac {\sqrt {a^2-2 a-4 c+1}}{m}+1\right ) J_{\frac {\sqrt {a^2-2 a-4 c+1}}{m}}\left (\frac {2 \sqrt {b} \sqrt {x^m}}{m}\right )\right \}\right \}\] ✓ Maple : cpu = 0.197 (sec), leaf count = 79
\[ \left \{ y \left ( x \right ) ={x}^{-{\frac {a}{2}}+{\frac {1}{2}}} \left ( {{\sl Y}_{{\frac {1}{m}\sqrt {{a}^{2}-2\,a-4\,c+1}}}\left (2\,{\frac {\sqrt {b}{x}^{m/2}}{m}}\right )}{\it \_C2}+{{\sl J}_{{\frac {1}{m}\sqrt {{a}^{2}-2\,a-4\,c+1}}}\left (2\,{\frac {\sqrt {b}{x}^{m/2}}{m}}\right )}{\it \_C1} \right ) \right \} \]