2.563   ODE No. 563

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

$$ay(x)+b+x{y}^{\prime }(x)+\log (y^{\prime }(x))=0$$ ✓ Mathematica : cpu = 0.136469 (sec), leaf count = 59

$$\text{Solve}[a(\frac{(a+1)\log (1-aW\left(x{e}^{-ay(x)-b}\right))}{a^2}+\frac{W\left(x{e}^{-ay(x)-b}\right)}{a})+ay(x)=c_1,y(x)]$$ ✓ Maple : cpu = 0.606 (sec), leaf count = 66

$$\{-{\left({\mathrm{e}}^{-ay\left(x\right)-\mathit{l}\mathit{a}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathit{t}\mathit{W}\left(x{\mathrm{e}}^{-ay\left(x\right)-b}\right)-b}\right)}^{-{(a+1)}^{-1}}\mathit{\_}\mathit{C}\mathit{1}+x-\frac{{\mathrm{e}}^{ay\left(x\right)+\mathit{l}\mathit{a}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathit{t}\mathit{W}\left(x{\mathrm{e}}^{-ay\left(x\right)-b}\right)+b}}{a}=0\}$$