\[ x y''(x)-x y'(x)-y(x)-e^x x (x+1)=0 \] ✓ Mathematica : cpu = 0.117987 (sec), leaf count = 45
DSolve[-(E^x*x*(1 + x)) - y[x] - x*Derivative[1][y][x] + x*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_2 \left (-e^x x \text {Ei}(-x)-1\right )+e^x \left (x^2+x-x \log (-x)-1\right )+c_1 e^x x\right \}\right \}\] ✓ Maple : cpu = 0.032 (sec), leaf count = 33
dsolve(x*diff(diff(y(x),x),x)-x*diff(y(x),x)-y(x)-x*(1+x)*exp(x)=0,y(x))
\[y \left (x \right ) = {\mathrm e}^{x} \left (-c_{1} x \Ei \left (1, x\right )+x^{2}+x c_{2}-x \ln \left (x \right )+c_{1} {\mathrm e}^{-x}-1\right )\]