What is the solution for y^{''}+4y=3sin(3t) ?

The solution for y^{''}+4y=3sin(3t) is y=c_{1}cos(2t)+c_{2}sin(2t)-3/5 sin(3t)

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y^{''}+4y=3sin(3t)

y^{^{''}} + 4 y = 3 sin (3 t)

y = c_{1} cos (2 t) + c_{2} sin (2 t) - \frac{3}{5} sin (3 t)

Solution steps

y^{''} (t) + 4 y = 3 sin (3 t)

Solve linear ODE:

y = c_{1} cos (2 t) + c_{2} sin (2 t) - \frac{3}{5} sin (3 t)

y = c_{1} cos (2 t) + c_{2} sin (2 t) - \frac{3}{5} sin (3 t)

y^{^{''}} + 9 y = cos (x) + \frac{1}{3} cos (3 x)

y^{^{''}} - 4 y^{^{'}} + 5 y = e^{2 x} sec^{3} (x)

y^{^{''}} - 9 y = (x^{2} - 4) sin (3 x)

y^{^{''}} + 8 y^{^{'}} = 64 x

y^{^{''}} + 5 y^{^{'}} + 4 y = e^{- x} + 2, y (0) = 1, y^{^{'}} (0) = 0

What is the solution for y^{''}+4y=3sin(3t) ?
The solution for y^{''}+4y=3sin(3t) is y=c_{1}cos(2t)+c_{2}sin(2t)-3/5 sin(3t)