\[ a x^{q-1} y'(x)+b x^{q-2} y(x)+y''(x)=0 \] ✓ Mathematica : cpu = 0.0261616 (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 = 2.393 (sec), leaf count = 81
\[ \left \{ y \left ( x \right ) ={{\rm e}^{-{\frac {{x}^{q}a}{q}}}}x \left ( {{\sl M}\left ({\frac {aq-b}{aq}},\,{\frac {q+1}{q}},\,{\frac {{x}^{q}a}{q}}\right )}{\it \_C1}+{{\sl U}\left ({\frac {aq-b}{aq}},\,{\frac {q+1}{q}},\,{\frac {{x}^{q}a}{q}}\right )}{\it \_C2} \right ) \right \} \]