What is the solution for y^{''}+9y=18sin(3t) ?

The solution for y^{''}+9y=18sin(3t) is y=c_{1}cos(3t)+c_{2}sin(3t)-3tcos(3t)

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y^{''}+9y=18sin(3t)

y^{^{''}} + 9 y = 18 sin (3 t)

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

Solution steps

y^{''} (t) + 9 y = 18 sin (3 t)

Solve linear ODE:

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

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

y^{^{''}} - y^{^{'}} - 6 y = 3 e^{2 x}

x^{^{''}} + 25 x = cos (t)

y^{^{''}} + 7 y^{^{'}} - 12 y = e^{3} x - 2 e^{x} - 5 x

y^{^{''}} - 4 y = t cos (2 t)

y^{^{'''}} + 2 y^{^{''}} + 2 y^{^{'}} = x^{2} - sin (x)

What is the solution for y^{''}+9y=18sin(3t) ?
The solution for y^{''}+9y=18sin(3t) is y=c_{1}cos(3t)+c_{2}sin(3t)-3tcos(3t)