\[ a x^{q-1} y'(x)+b x^{q-2} y(x)+y''(x)=0 \] ✓ Mathematica : cpu = 0.0256687 (sec), leaf count = 83
DSolve[b*x^(-2 + q)*y[x] + a*x^(-1 + q)*Derivative[1][y][x] + Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_2 q^{-1/q} a^{\frac {1}{q}} \left (x^q\right )^{\frac {1}{q}} \, _1F_1\left (\frac {b}{a q}+\frac {1}{q};1+\frac {1}{q};-\frac {a x^q}{q}\right )+c_1 \, _1F_1\left (\frac {b}{a q};1-\frac {1}{q};-\frac {a x^q}{q}\right )\right \}\right \}\] ✓ Maple : cpu = 0.162 (sec), leaf count = 81
dsolve(diff(diff(y(x),x),x)+a*x^(q-1)*diff(y(x),x)+b*x^(q-2)*y(x)=0,y(x))
\[y \left (x \right ) = {\mathrm e}^{-\frac {x^{q} a}{q}} x \left (\KummerM \left (\frac {a q -b}{a q}, \frac {q +1}{q}, \frac {x^{q} a}{q}\right ) c_{1}+\KummerU \left (\frac {a q -b}{a q}, \frac {q +1}{q}, \frac {x^{q} a}{q}\right ) c_{2}\right )\]