en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(dy)/(dt)=ky+n

Solution

\frac{d y}{d t} = k y + n

Solution

y = \frac{e ^{t k + c_{1}}}{k} - \frac{n}{k}

Solution steps

\frac{d y}{d t} = k y (t) + n

Solve separable ODE:

y = \frac{e ^{t k + c_{1}}}{k} - \frac{n}{k}

y = \frac{e ^{t k + c_{1}}}{k} - \frac{n}{k}

Popular Examples

sqrt(x)(dy)/(dx)=e^{2y+sqrt(x)}

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

y^'=((5x^2-1))/(5+4y)

y^{^{'}} = \frac{( 5 x ^{2} - 1 )}{5 + 4 y}

y^{^{'}} - 5 y = 15

y^'+4y=1.4,y(0)=ce^{-4x}+0.35,y(0)=2

y^{^{'}} + 4 y = 1.4, y (0) = c e^{- 4 x} + 0.35, y (0) = 2

(dy)/(dx)=-5/5 x^7y^6

\frac{d y}{d x} = - \frac{5}{5} x^{7} y^{6}

Frequently Asked Questions (FAQ)

What is the solution for (dy)/(dt)=ky+n ?
The solution for (dy)/(dt)=ky+n is y=(e^{tk+c_{1}})/k-n/k