en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(dx)/(dt)=r-kx

Solution

\frac{d x}{d t} = r - k x

Solution

x = - \frac{e ^{- k t - c_{1}}}{k} + \frac{r}{k}

Solution steps

\frac{d x}{d t} = r - k x (t)

Solve separable ODE:

x = - \frac{e ^{- k t - c_{1}}}{k} + \frac{r}{k}

x = - \frac{e ^{- k t - c_{1}}}{k} + \frac{r}{k}

Popular Examples

(dy)/(dx)=5y,y(2)=2

\frac{d y}{d x} = 5 y, y (2) = 2

3y^2(dy)/(dx)=4x^3

3 y^{2} \frac{d y}{d x} = 4 x^{3}

y^{^{'}} + a b^{2} y = 0

(dy)/(dx)=((3x^2-e^x))/(2y-5),y(0)=1

\frac{d y}{d x} = \frac{( 3 x ^{2} - e ^{x} )}{2 y - 5}, y (0) = 1

(dy)/(dx)=10-y/(50)

\frac{d y}{d x} = 10 - \frac{y}{50}

Frequently Asked Questions (FAQ)

What is the solution for (dx)/(dt)=r-kx ?
The solution for (dx)/(dt)=r-kx is x=-(e^{-kt-c_{1}})/k+r/k