en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''}+ay^'=b

Solution

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

Solution

y = c_{1} + c_{2} e^{- a t} + \frac{b t}{a}

Solution steps

y^{''} (t) + a y^{'} (t) = b

Solve linear ODE:

y = c_{1} + c_{2} e^{- a t} + \frac{b t}{a}

y = c_{1} + c_{2} e^{- a t} + \frac{b t}{a}

Popular Examples

y^{''}-8y^'+16y=10e^{4x}sec(x)

y^{^{''}} - 8 y^{^{'}} + 16 y = 10 e^{4 x} sec (x)

y^{''}+3y^'+2y=xsin(x)

y^{^{''}} + 3 y^{^{'}} + 2 y = x sin (x)

y^{''}+4y=cos^2(x)

y^{^{''}} + 4 y = cos^{2} (x)

y^{''}+4y^'+6y=1+e^{-t}

y^{^{''}} + 4 y^{^{'}} + 6 y = 1 + e^{- t}

y^{''}-2y^'-3y=8e^x-3

y^{^{''}} - 2 y^{^{'}} - 3 y = 8 e^{x} - 3

Frequently Asked Questions (FAQ)

What is the solution for y^{''}+ay^'=b ?
The solution for y^{''}+ay^'=b is y=c_{1}+c_{2}e^{-at}+(bt)/a