4.100   ODE No. 1100

$$\boxed{{\displaystyle x\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+2\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-xy\left(x\right)-{\mathrm{e}}^x=0}}$$

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

Mathematica: cpu = 0.021503 (sec), leaf count = 44 $$\left\{\{y(x)\to \frac{c_1{e}^{-x}}{x}+\frac{c_2{e}^x}{2x}+\frac{e^x(2x-1)}{4x}\}\right\}$$

Maple: cpu = 0.032 (sec), leaf count = 23 $$\{y\left(x\right)=\frac{\sinh \left(x\right)\mathit{\_}\mathit{C}\mathit{2}}{x}+\frac{\cosh \left(x\right)\mathit{\_}\mathit{C}\mathit{1}}{x}+\frac{{\mathrm{e}}^x}{2}\}$$