\[ \boxed { x{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -2\, \left ( ax+b \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( {a}^{2}x+2\,ab \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.174522 (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 = 0.047 (sec), leaf count = 24 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{ax}}+{\it \_C2}\,{x }^{2\,b+1}{{\rm e}^{ax}} \right \} \]