\[ a x^{q-1} y'(x)+b x^{q-2} y(x)+y''(x)=0 \] ✓ Mathematica : cpu = 0.0306881 (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 = 0.293 (sec), leaf count = 81
\[\left \{y \left (x \right ) = \left (c_{1} \KummerM \left (\frac {a q -b}{a q}, \frac {q +1}{q}, \frac {a \,x^{q}}{q}\right )+c_{2} \KummerU \left (\frac {a q -b}{a q}, \frac {q +1}{q}, \frac {a \,x^{q}}{q}\right )\right ) x \,{\mathrm e}^{-\frac {a \,x^{q}}{q}}\right \}\]