\[ x^2 y''(x)+\frac {y(x)}{\log (x)}-e^x x (x \log (x)+2)=0 \] ✓ Mathematica : cpu = 0.0781277 (sec), leaf count = 32
DSolve[-(E^x*x*(2 + x*Log[x])) + y[x]/Log[x] + x^2*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_2 \log (x) \left (\text {li}(x)-\frac {x}{\log (x)}\right )+e^x \log (x)+c_1 \log (x)\right \}\right \}\] ✓ Maple : cpu = 0.144 (sec), leaf count = 71
dsolve(x^2*diff(diff(y(x),x),x)+y(x)/ln(x)-x*exp(x)*(2+x*ln(x))=0,y(x))
\[y \left (x \right ) = c_{2} \ln \left (x \right )-\left (\Ei \left (1, -\ln \left (x \right )\right ) \ln \left (x \right )+x \right ) c_{1}-\ln \left (x \right ) \left (-\left (\int \frac {\left (\Ei \left (1, -\ln \left (x \right )\right ) \ln \left (x \right )+x \right ) {\mathrm e}^{x} \left (2+x \ln \left (x \right )\right )}{x}d x \right )+{\mathrm e}^{x} \ln \left (x \right ) \left (\Ei \left (1, -\ln \left (x \right )\right ) \ln \left (x \right )+x \right )\right )\]