\[ \boxed { {x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +{\frac {y \left ( x \right ) }{\ln \left ( x \right ) }}-x{{\rm e}^{x}} \left ( 2+x\ln \left ( x \right ) \right ) =0} \]
Mathematica: cpu = 0.207026 (sec), leaf count = 34 \[ \text {DSolve}\left [x^2 y''(x)+\frac {y(x)}{\log (x)}-e^x x (x \log (x)+2)=0,y(x),x\right ] \]
Maple: cpu = 0.093 (sec), leaf count = 73 \[ \left \{ y \left ( x \right ) =\ln \left ( x \right ) {\it \_C2}+ \left ( -{\it Ei} \left ( 1,-\ln \left ( x \right ) \right ) \ln \left ( x \right ) -x \right ) {\it \_C1}- \left ( -\int \!{\frac { \left ( {\it Ei } \left ( 1,-\ln \left ( x \right ) \right ) \ln \left ( x \right ) +x \right ) {{\rm e}^{x}} \left ( 2+x\ln \left ( x \right ) \right ) }{x}} \,{\rm d}x+{{\rm e}^{x}}\ln \left ( x \right ) \left ( {\it Ei} \left ( 1,-\ln \left ( x \right ) \right ) \ln \left ( x \right ) +x \right ) \right ) \ln \left ( x \right ) \right \} \]