2.1109   ODE No. 1109

1. Problem in Latex
2. Mathematica input
3. Maple input

$$x{y}^{″}(x)-x{y}^{\prime }(x)-y(x)-e^{x}x(x+1)=0$$ ✓ Mathematica : cpu = 0.0534357 (sec), leaf count = 45

$$\left\{\{y(x)\to c_2(-e^{x}x\text{Ei}(-x)-1)+c_1{e}^{x}x+e^x(x^2+x-x\log (-x)-1)\}\right\}$$

✓ Maple : cpu = 0.03 (sec), leaf count = 40

$$\{y\left(x\right)=(-x\mathit{E}\mathit{i}(1,x)+{\mathrm{e}}^{-x}){\mathrm{e}}^x\mathit{\_}\mathit{C}\mathit{1}+{\mathrm{e}}^x\mathit{\_}\mathit{C}\mathit{2}x-(x\ln \left(x\right)-x^2+1){\mathrm{e}}^x\}$$