What is the solution for y^{''}+36y=-36sin(6t) ?

The solution for y^{''}+36y=-36sin(6t) is y=c_{1}cos(6t)+c_{2}sin(6t)+3tcos(6t)

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y^{''}+36y=-36sin(6t)

y^{^{''}} + 36 y = - 36 sin (6 t)

y = c_{1} cos (6 t) + c_{2} sin (6 t) + 3 t cos (6 t)

Solution steps

y^{''} (t) + 36 y = - 36 sin (6 t)

Solve linear ODE:

y = c_{1} cos (6 t) + c_{2} sin (6 t) + 3 t cos (6 t)

y = c_{1} cos (6 t) + c_{2} sin (6 t) + 3 t cos (6 t)

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

y^{^{''}} + 4 y^{^{'}} + 4 y = (x + 1) e^{2 x}

y^{^{''}} + 9 y = 2 x^{2} - 5

y^{^{'''}} - y^{^{''}} = 4 x + 2 x e^{- 2 x}

y^{^{''}} - 8 y^{^{'}} + 16 y = 4 e^{4 x} ln (x)

What is the solution for y^{''}+36y=-36sin(6t) ?
The solution for y^{''}+36y=-36sin(6t) is y=c_{1}cos(6t)+c_{2}sin(6t)+3tcos(6t)