en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

(dy)/(dt)=e^{-y}

Solution

\frac{d y}{d t} = e^{- y}

Solution

y = ln (t + c_{1})

Solution steps

\frac{d y}{d t} = e^{- y}

Solve separable ODE:

y = ln (t + c_{1})

y = ln (t + c_{1})

Graph

Popular Examples

integral of 1/9 e^{9x}

\int \frac{1}{9} e^{9 x} d x

derivative of (6x^2+1/(x^2+9))

\frac{d}{d x} (\frac{6 x ^{2} + 1}{x ^{2} + 9})

- y^{^{''}} = 1

integral of (5x^3-9sqrt(x))/x

\int \frac{5 x ^{3} - 9 x}{x} d x

integral of (25)/((x-1)(x^2+4))

\int \frac{25}{( x - 1 ) ( x ^{2} + 4 )} d x

Frequently Asked Questions (FAQ)

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