2.1060   ODE No. 1060

\[ a x^{q-1} y'(x)+b x^{q-2} y(x)+y''(x)=0 \]

✓ Mathematica : cpu = 0.0206432 (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 = 0.275 (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))
 

\[y \left (x \right ) = {\mathrm e}^{-\frac {a \,x^{q}}{q}} x \left (\operatorname {KummerU}\left (\frac {a q -b}{a q}, \frac {q +1}{q}, \frac {a \,x^{q}}{q}\right ) c_{2} +\operatorname {KummerM}\left (\frac {a q -b}{a q}, \frac {q +1}{q}, \frac {a \,x^{q}}{q}\right ) c_{1} \right )\]