\[ x^2 y''(x)+\frac {y(x)}{\log (x)}-e^x x (x \log (x)+2)=0 \] ✓ Mathematica : cpu = 0.0781277 (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 = 0.144 (sec), leaf count = 71
\[y \relax (x ) = c_{2} \ln \relax (x )-\left (\Ei \left (1, -\ln \relax (x )\right ) \ln \relax (x )+x \right ) c_{1}-\ln \relax (x ) \left (-\left (\int \frac {\left (\Ei \left (1, -\ln \relax (x )\right ) \ln \relax (x )+x \right ) {\mathrm e}^{x} \left (2+x \ln \relax (x )\right )}{x}d x \right )+{\mathrm e}^{x} \ln \relax (x ) \left (\Ei \left (1, -\ln \relax (x )\right ) \ln \relax (x )+x \right )\right )\]