Resolver y=e^x+y^2

$$y = e ^ { x } + y ^ { 2 }$$

Ebatzi: x (complex solution)

$$x=\ln(y\left(1-y\right))+2i\pi n_{1}$$

$$n_{1}\in \mathrm{Z}$$

$$y\neq 1\text{ and }y\neq 0$$

Ebatzi: y (complex solution)

$$y=\frac{-\sqrt{1-4e^{x}}+1}{2}$$

$$y=\frac{\sqrt{1-4e^{x}}+1}{2}$$

Ebatzi: x

$$x=\ln(y\left(1-y\right))$$

$$y>0\text{ and }y<1$$

Ebatzi: y

$$y=\frac{-\sqrt{1-4e^{x}}+1}{2}$$

$$y=\frac{\sqrt{1-4e^{x}}+1}{2}\text{, }x\leq -2\ln(2)$$