What is the solution for y^{''}+36y=-12sin(6t) ?

The solution for y^{''}+36y=-12sin(6t) is y=c_{1}cos(6t)+c_{2}sin(6t)+tcos(6t)

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y^{''}+36y=-12sin(6t)

y^{^{''}} + 36 y = - 12 sin (6 t)

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

Solution steps

y^{''} (t) + 36 y = - 12 sin (6 t)

Solve linear ODE:

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

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

y^{^{''}} - 3 y^{^{'}} + 2 y = 6 e^{- t}

y^{^{''}} + 3 y = x^{2} sin (x) cos (x)

0.5 y^{^{''}} + 6 y^{^{'}} + 50 y = 24 sin (10 t)

y^{^{''}} + 2 y^{^{'}} + 2 y = 2

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

What is the solution for y^{''}+36y=-12sin(6t) ?
The solution for y^{''}+36y=-12sin(6t) is y=c_{1}cos(6t)+c_{2}sin(6t)+tcos(6t)