\[ x y''(x)-x y'(x)-y(x)-e^x x (x+1)=0 \] ✓ Mathematica : cpu = 0.133269 (sec), leaf count = 45
\[\left \{\left \{y(x)\to c_2 \left (-e^x x \text {Ei}(-x)-1\right )+e^x \left (x^2+x-x \log (-x)-1\right )+c_1 e^x x\right \}\right \}\] ✓ Maple : cpu = 0.034 (sec), leaf count = 33
\[\{y \left (x \right ) = \left (-c_{1} x \Ei \left (1, x\right )+c_{1} {\mathrm e}^{-x}+c_{2} x +x^{2}-x \ln \left (x \right )-1\right ) {\mathrm e}^{x}\}\]