\[ \boxed { {x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( a{x}^{m}+b \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.082010 (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 = 0.031 (sec), leaf count = 63 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,x{{\sl J}_{2\,{\frac {\sqrt { 1-b}}{m}}}\left (2\,{\frac {\sqrt {a}{x}^{m/2}}{m}}\right )}+{\it \_C2} \,x{{\sl Y}_{2\,{\frac {\sqrt {1-b}}{m}}}\left (2\,{\frac {\sqrt {a}{x} ^{m/2}}{m}}\right )} \right \} \]