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)

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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)

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)