\[ y(x) \left (a^2 x+2 a b\right )-2 (a x+b) y'(x)+x y''(x)=0 \] ✓ Mathematica : cpu = 0.106843 (sec), leaf count = 77
\[\left \{\left \{y(x)\to c_1 e^{a x} x^{b-\frac {1}{2} \sqrt {(2 b+1)^2}+\frac {1}{2}}+\frac {c_2 e^{a x} x^{b+\frac {1}{2} \sqrt {(2 b+1)^2}+\frac {1}{2}}}{\sqrt {(2 b+1)^2}}\right \}\right \}\] ✓ Maple : cpu = 0.042 (sec), leaf count = 20
\[y \relax (x ) = {\mathrm e}^{a x} \left (x^{2 b +1} c_{2}+c_{1}\right )\]