What is the solution for y^{''}+2y^'=2x ?

The solution for y^{''}+2y^'=2x is y=c_{1}+c_{2}e^{-2x}+(x^2)/2-x/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''}+2y^'=2x

y^{^{''}} + 2 y^{^{'}} = 2 x

y = c_{1} + c_{2} e^{- 2 x} + \frac{x ^{2}}{2} - \frac{x}{2}

Solution steps

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

Solve linear ODE:

y = c_{1} + c_{2} e^{- 2 x} + \frac{x ^{2}}{2} - \frac{x}{2}

y = c_{1} + c_{2} e^{- 2 x} + \frac{x ^{2}}{2} - \frac{x}{2}

y^{^{''}} + 4 y^{^{'}} + 4 y = e^{- 2 t} ln (t)

y^{^{''}} + 2 y^{^{'}} + y = e - t

y^{^{'''}} + 4 y^{^{'}} = 4 x^{2} + 8 x

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

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

What is the solution for y^{''}+2y^'=2x ?
The solution for y^{''}+2y^'=2x is y=c_{1}+c_{2}e^{-2x}+(x^2)/2-x/2