What is the solution for y^{''}+6y^'+5y=-1020sin(3t) ?

The solution for y^{''}+6y^'+5y=-1020sin(3t) is y=c_{1}e^{-t}+c_{2}e^{-5t}+12sin(3t)+54cos(3t)

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y^{''}+6y^'+5y=-1020sin(3t)

y^{^{''}} + 6 y^{^{'}} + 5 y = - 1020 sin (3 t)

y = c_{1} e^{- t} + c_{2} e^{- 5 t} + 12 sin (3 t) + 54 cos (3 t)

Solution steps

y^{''} (t) + 6 y^{'} (t) + 5 y = - 1020 sin (3 t)

Solve linear ODE:

y = c_{1} e^{- t} + c_{2} e^{- 5 t} + 12 sin (3 t) + 54 cos (3 t)

y = c_{1} e^{- t} + c_{2} e^{- 5 t} + 12 sin (3 t) + 54 cos (3 t)

y^{^{''}} + 2 y^{^{'}} - 8 y = 4 a

(D^{2} + 4 D + 8) y = 4 sin (2 x)

y^{^{''}} + 9 y = 2 t^{2} - 2, y (0) = 0, y^{^{'}} (0) = - 8

y^{^{'''}} + 3 y^{^{''}} - y^{^{'}} - 3 y = 3 x - 14

y^{^{''}} - 16 y^{^{'}} + 64 y = - \frac{2}{3 x} e^{8 x}

What is the solution for y^{''}+6y^'+5y=-1020sin(3t) ?
The solution for y^{''}+6y^'+5y=-1020sin(3t) is y=c_{1}e^{-t}+c_{2}e^{-5t}+12sin(3t)+54cos(3t)