Решете y=y_{0}(1-e^-xy)

$$y = y _ { 0 } ( 1 - e ^ { - x y } )$$

Решаване за x (complex solution)

$$\left\{\begin{matrix}x=-\frac{2\pi n_{1}i}{y}-\frac{\ln(\frac{y_{0}-y}{y_{0}})}{y}\text{, }n_{1}\in \mathrm{Z}\text{, }&y\neq 0\text{ and }y\neq y_{0}\text{ and }y_{0}\neq 0\\x\in \mathrm{C}\text{, }&y=0\end{matrix}\right,$$

Решаване за x

$$\left\{\begin{matrix}x=-\frac{\ln(\frac{y_{0}-y}{y_{0}})}{y}\text{, }&\left(y\neq 0\text{ and }y>y_{0}\text{ and }y_{0}<0\right)\text{ or }\left(y\neq 0\text{ and }y<y_{0}\text{ and }y_{0}>0\right)\\x\in \mathrm{R}\text{, }&y=0\end{matrix}\right,$$