3.719   ODE No. 719

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

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

Mathematica: cpu = 0.100013 (sec), leaf count = 49 $$\left\{\{y(x)\to \frac{2^{e^{-x}}{x}^{e^{-x}-1}}{c_1{e}^{\text{Ei}(-x)}+2^{e^{-x}}{x}^{e^{-x}}}\}\right\}$$

Maple: cpu = 0.110 (sec), leaf count = 57 $$\{y\left(x\right)=-\frac{x^{{\mathrm{e}}^{-x}}{2}^{{\mathrm{e}}^{-x}}{\mathrm{e}}^{\mathit{E}\mathit{i}(1,x)}}{x(\int x^{{\mathrm{e}}^{-x}}{2}^{{\mathrm{e}}^{-x}}{\mathrm{e}}^{\mathit{E}\mathit{i}(1,x)}{\mathrm{e}}^{-x}(\ln \left(2\right)+\ln \left(x\right))\mathrm{d}x+\mathit{\_}\mathit{C}\mathit{1})}\}$$