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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

y = ln (e^{x} - x + c_{1})

Solution steps

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

Solve separable ODE:

y = ln (e^{x} - x + c_{1})

y = ln (e^{x} - x + c_{1})

\frac{\partial}{\partial y} (1 + ln (x) + \frac{y}{x})

\int e^{4 x^{2}} d x

\frac{d x}{d y} = \frac{x}{y}

\frac{\partial}{\partial y} (\frac{18 x y}{x + y})

arccsc (x^{4} + 1)

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