y=e^a-x^e eching

$$y = e ^ { a } - x ^ { e }$$

a uchun yechish (complex solution)

$$a=\ln(x^{e}+y)+2\pi n_{1}i$$

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

$$y\neq -x^{e}$$

x uchun yechish (complex solution)

$$x=\left(|y-e^{a}|\right)^{\frac{1}{e}}e^{\frac{iarg(e^{a}-y)}{e}-\frac{2i\pi n_{1}}{e}}$$

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

a uchun yechish

$$a=\ln(x^{e}+y)$$

$$\left(y>-x^{e}\text{ and }x>0\right)\text{ or }\left(y>0\text{ and }x=0\right)$$

x uchun yechish

$$x=\left(e^{a}-y\right)^{\frac{1}{e}}$$

$$y=e^{a}\text{ or }\left(e^{a}-y\geq 0\text{ and }\left(e^{a}-y\right)^{\frac{1}{e}}>0\text{ and }y<e^{a}\right)$$