2.719   ODE No. 719

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

$$y^{\prime }(x)=\frac{e^{-x}y(x)(x^{2}y(x)\log (2x)-e^x-x\log (2x))}{x}$$ ✓ Mathematica : cpu = 0.364543 (sec), leaf count = 49

$$\left\{\{y(x)\to \frac{2^{e^{-x}}{x}^{e^{-x}-1}}{2^{e^{-x}}{x}^{e^{-x}}+c_1{e}^{\text{Ei}(-x)}}\}\right\}$$ ✓ Maple : cpu = 0.338 (sec), leaf count = 34

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