\[ x^2 y''(x)+\frac {y(x)}{\log (x)}-e^x x (x \log (x)+2)=0 \] ✓ Mathematica : cpu = 0.0846221 (sec), leaf count = 32
\[\left \{\left \{y(x)\to c_2 \log (x) \left (\text {li}(x)-\frac {x}{\log (x)}\right )+e^x \log (x)+c_1 \log (x)\right \}\right \}\] ✓ Maple : cpu = 0.197 (sec), leaf count = 71
\[ \left \{ y \left ( x \right ) =\ln \left ( x \right ) {\it \_C2}- \left ( {\it Ei} \left ( 1,-\ln \left ( x \right ) \right ) \ln \left ( x \right ) +x \right ) {\it \_C1}- \left ( -\int \!{\frac { \left ( {\it Ei} \left ( 1,-\ln \left ( x \right ) \right ) \ln \left ( x \right ) +x \right ) {{\rm e}^{x}} \left ( 2+x\ln \left ( x \right ) \right ) }{x}}\,{\rm d}x+{{\rm e}^{x}}\ln \left ( x \right ) \left ( {\it Ei} \left ( 1,-\ln \left ( x \right ) \right ) \ln \left ( x \right ) +x \right ) \right ) \ln \left ( x \right ) \right \} \]