What is the solution for y^{''}-y^'-6y=-468sin(3t) ?

The solution for y^{''}-y^'-6y=-468sin(3t) is y=c_{1}e^{3t}+c_{2}e^{-2t}+30sin(3t)-6cos(3t)

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y^{''}-y^'-6y=-468sin(3t)

y^{^{''}} - y^{^{'}} - 6 y = - 468 sin (3 t)

y = c_{1} e^{3 t} + c_{2} e^{- 2 t} + 30 sin (3 t) - 6 cos (3 t)

Solution steps

y^{''} (t) - y^{'} (t) - 6 y = - 468 sin (3 t)

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} e^{- 2 t} + 30 sin (3 t) - 6 cos (3 t)

y = c_{1} e^{3 t} + c_{2} e^{- 2 t} + 30 sin (3 t) - 6 cos (3 t)

3 y^{^{''}} - 4 y^{^{'}} + y = 5

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

(D^{2} + 2 D + 1) y = \frac{e ^{- x}}{x}

y^{^{''}} + 4 y^{^{'}} + 3 y = 64 e^{t}, y (0) = 4, y^{^{'}} (0) = 7

x^{^{''}} + x^{^{'}} + 2 x = sin (t)

What is the solution for y^{''}-y^'-6y=-468sin(3t) ?
The solution for y^{''}-y^'-6y=-468sin(3t) is y=c_{1}e^{3t}+c_{2}e^{-2t}+30sin(3t)-6cos(3t)