What is the solution for y^{''}+8y^'+16y=8sin(2t) ?

The solution for y^{''}+8y^'+16y=8sin(2t) is y=c_{1}e^{-4t}+c_{2}te^{-4t}+6/25 sin(2t)-8/25 cos(2t)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''}+8y^'+16y=8sin(2t)

y^{^{''}} + 8 y^{^{'}} + 16 y = 8 sin (2 t)

y = c_{1} e^{- 4 t} + c_{2} t e^{- 4 t} + \frac{6}{25} sin (2 t) - \frac{8}{25} cos (2 t)

Solution steps

y^{''} (t) + 8 y^{'} (t) + 16 y = 8 sin (2 t)

Solve linear ODE:

y = c_{1} e^{- 4 t} + c_{2} t e^{- 4 t} + \frac{6}{25} sin (2 t) - \frac{8}{25} cos (2 t)

y = c_{1} e^{- 4 t} + c_{2} t e^{- 4 t} + \frac{6}{25} sin (2 t) - \frac{8}{25} cos (2 t)

y^{^{''}} - 4 y = x^{3}

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

y^{^{''}} - 2 y^{^{'}} + y = 12 x^{3} e^{x}

2 y^{^{''}} - 2 y^{^{'}} - 4 y = 2 e^{2 t}

y^{^{'''}} - 6 y^{^{''}} - 6 = cos (x)

What is the solution for y^{''}+8y^'+16y=8sin(2t) ?
The solution for y^{''}+8y^'+16y=8sin(2t) is y=c_{1}e^{-4t}+c_{2}te^{-4t}+6/25 sin(2t)-8/25 cos(2t)