\[ y(x) \left (a x^m+b\right )+x^2 y''(x)-x y'(x)=0 \] ✓ Mathematica : cpu = 0.0549623 (sec), leaf count = 326
\[\left \{\left \{y(x)\to c_1 m^{-\frac {2 \left (m-i \sqrt {b-1} m\right )}{m^2}-\frac {2 i \sqrt {b-1}}{m}} a^{\frac {m-i \sqrt {b-1} m}{m^2}+\frac {i \sqrt {b-1}}{m}} \left (x^m\right )^{\frac {m-i \sqrt {b-1} m}{m^2}+\frac {i \sqrt {b-1}}{m}} \Gamma \left (1-\frac {2 i \sqrt {b-1}}{m}\right ) J_{-\frac {2 i \sqrt {b-1}}{m}}\left (\frac {2 \sqrt {a} \sqrt {x^m}}{m}\right )+c_2 m^{\frac {2 i \sqrt {b-1}}{m}-\frac {2 \left (m+i \sqrt {b-1} m\right )}{m^2}} a^{\frac {m+i \sqrt {b-1} m}{m^2}-\frac {i \sqrt {b-1}}{m}} \left (x^m\right )^{\frac {m+i \sqrt {b-1} m}{m^2}-\frac {i \sqrt {b-1}}{m}} \Gamma \left (\frac {2 i \sqrt {b-1}}{m}+1\right ) J_{\frac {2 i \sqrt {b-1}}{m}}\left (\frac {2 \sqrt {a} \sqrt {x^m}}{m}\right )\right \}\right \}\] ✓ Maple : cpu = 0.038 (sec), leaf count = 63
\[y \relax (x ) = x \left (\BesselY \left (\frac {2 \sqrt {1-b}}{m}, \frac {2 \sqrt {a}\, x^{\frac {m}{2}}}{m}\right ) c_{2}+\BesselJ \left (\frac {2 \sqrt {1-b}}{m}, \frac {2 \sqrt {a}\, x^{\frac {m}{2}}}{m}\right ) c_{1}\right )\]