\[ x^2 y''(x)+\frac {y(x)}{\log (x)}-e^x x (x \log (x)+2)=0 \] ✓ Mathematica : cpu = 0.0916499 (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 = 0.247 (sec), leaf count = 71
\[\left \{y \left (x \right ) = c_{2} \ln \left (x \right )-c_{1} \left (\Ei \left (1, -\ln \left (x \right )\right ) \ln \left (x \right )+x \right )-\left (\left (\Ei \left (1, -\ln \left (x \right )\right ) \ln \left (x \right )+x \right ) {\mathrm e}^{x} \ln \left (x \right )-\left (\int \frac {\left (\Ei \left (1, -\ln \left (x \right )\right ) \ln \left (x \right )+x \right ) \left (x \ln \left (x \right )+2\right ) {\mathrm e}^{x}}{x}d x \right )\right ) \ln \left (x \right )\right \}\]