What is the solution for y^{''}+6y^'+9y=4sin(6t) ?

The solution for y^{''}+6y^'+9y=4sin(6t) is y=c_{1}e^{-3t}+c_{2}te^{-3t}-4/75 sin(6t)-16/225 cos(6t)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''}+6y^'+9y=4sin(6t)

y^{^{''}} + 6 y^{^{'}} + 9 y = 4 sin (6 t)

y = c_{1} e^{- 3 t} + c_{2} t e^{- 3 t} - \frac{4}{75} sin (6 t) - \frac{16}{225} cos (6 t)

Solution steps

y^{''} (t) + 6 y^{'} (t) + 9 y = 4 sin (6 t)

Solve linear ODE:

y = c_{1} e^{- 3 t} + c_{2} t e^{- 3 t} - \frac{4}{75} sin (6 t) - \frac{16}{225} cos (6 t)

y = c_{1} e^{- 3 t} + c_{2} t e^{- 3 t} - \frac{4}{75} sin (6 t) - \frac{16}{225} cos (6 t)

y^{^{''}} + 9 y = t + 3, y (0) = 1, y^{^{'}} (0) = 2

y^{^{''}} - 5 y^{^{'}} + 2 y = 6 t^{2} + 2 t + 7

y^{^{''}} + 5 y^{^{'}} + 80 y = 220 cos (11 t)

y^{^{''}} - y = - 1

y^{^{''}} + 10 y^{^{'}} + 16 = 10

What is the solution for y^{''}+6y^'+9y=4sin(6t) ?
The solution for y^{''}+6y^'+9y=4sin(6t) is y=c_{1}e^{-3t}+c_{2}te^{-3t}-4/75 sin(6t)-16/225 cos(6t)