What is the solution for y^{''}+36y=24sin(6t) ?

The solution for y^{''}+36y=24sin(6t) is y=c_{1}cos(6t)+c_{2}sin(6t)-2tcos(6t)

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y^{''}+36y=24sin(6t)

y^{^{''}} + 36 y = 24 sin (6 t)

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

Solution steps

y^{''} (t) + 36 y = 24 sin (6 t)

Solve linear ODE:

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

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

y^{^{'''}} - 9 y^{^{'}} = t e^{- 3 t} + 4 cos (3 t)

0.05 y^{^{''}} - 0.3 y^{^{'}} + 0.4 y = 11

y^{^{''}} + 4 y = - 6

y^{^{''}} + y = sec^{2} (t)

y^{^{''}} - 12 y^{^{'}} + 36 y = 6 e^{6 x}

What is the solution for y^{''}+36y=24sin(6t) ?
The solution for y^{''}+36y=24sin(6t) is y=c_{1}cos(6t)+c_{2}sin(6t)-2tcos(6t)