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

Popular >

(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

8 x \frac{d y}{d x} = 2 x e^{x} - 8 y + 6 x^{2}

\frac{sec ( 9 x )}{1 + sec ( 9 x )}

\frac{\partial}{\partial x} (\frac{- x - 9 y}{2 y - 7 x})

\frac{d}{d x} (3 sin (x) - 4 sin^{3} (x))

x \to 0 + lim (\frac{1}{1 - e ^{x}} - \frac{1}{x})

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