What is the solution for (1+e^x)y(dy)/(dx)=e^y ?

The solution for (1+e^x)y(dy)/(dx)=e^y is y=-\W((-ln(1+e^x)+x+c_{1})/e)-1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(1+e^x)y(dy)/(dx)=e^y

(1 + e^{x}) y \frac{d y}{d x} = e^{y}

y = - W (\frac{- ln ( 1 + e ^{x} ) + x + c _{1}}{e}) - 1

Solution steps

(1 + e^{x}) y \frac{d y}{d x} = e^{y}

Solve separable ODE:

y = - W (\frac{- ln ( 1 + e ^{x} ) + x + c _{1}}{e}) - 1

y = - W (\frac{- ln ( 1 + e ^{x} ) + x + c _{1}}{e}) - 1

What is the solution for (1+e^x)y(dy)/(dx)=e^y ?
The solution for (1+e^x)y(dy)/(dx)=e^y is y=-\W((-ln(1+e^x)+x+c_{1})/e)-1