2.565   ODE No. 565

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

$$y^{\prime }(x)+y(x)\log (y^{\prime }(x))-xy(x)-y(x)\log (y(x))=0$$ ✓ Mathematica : cpu = 0.0301469 (sec), leaf count = 25

$$\left\{\{y(x)\to c_1{e}^{\frac{1}{2}W{\left(e^x\right)}^2+W\left(e^x\right)}\}\right\}$$ ✓ Maple : cpu = 0.257 (sec), leaf count = 17

$$\{y\left(x\right)=c_1{\mathrm{e}}^{\frac{(\mathrm{LambertW}\left({\mathrm{e}}^x\right)+2)\mathrm{LambertW}\left({\mathrm{e}}^x\right)}{2}}\}$$