\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +a{x}^{q-1}{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +b{x}^{q-2}y \left ( x \right ) =0} \]
Mathematica: cpu = 0.037005 (sec), leaf count = 83 \[ \left \{\left \{y(x)\to c_2 q^{-1/q} a^{\frac {1}{q}} \left (x^q\right )^{\frac {1}{q}} \, _1F_1\left (\frac {b}{a q}+\frac {1}{q};1+\frac {1}{q};-\frac {a x^q}{q}\right )+c_1 \, _1F_1\left (\frac {b}{a q};1-\frac {1}{q};-\frac {a x^q}{q}\right )\right \}\right \} \]
Maple: cpu = 0.125 (sec), leaf count = 91 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{-{\frac {a{x}^{q}}{ q}}}}{{\sl M}\left ({\frac {aq-b}{aq}},\,{\frac {q+1}{q}},\,{\frac {a{x }^{q}}{q}}\right )}x+{\it \_C2}\,{{\rm e}^{-{\frac {a{x}^{q}}{q}}}}{ {\sl U}\left ({\frac {aq-b}{aq}},\,{\frac {q+1}{q}},\,{\frac {a{x}^{q} }{q}}\right )}x \right \} \]