\[ \boxed { {x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -2\,x \left ( 1+x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +2\, \left ( 1+x \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.014502 (sec), leaf count = 22 \[ \left \{\left \{y(x)\to c_1 x+\frac {1}{2} c_2 e^{2 x} x\right \}\right \} \]
Maple: cpu = 0.031 (sec), leaf count = 15 \[ \left \{ y \left ( x \right ) =x{\it \_C1}+{\it \_C2}\,x{{\rm e}^{2\,x}} \right \} \]