What is the solution for 5y^{''}+180y=150sin(3t) ?

The solution for 5y^{''}+180y=150sin(3t) is y=c_{1}cos(6t)+c_{2}sin(6t)+10/9 sin(3t)

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5y^{''}+180y=150sin(3t)

5 y^{^{''}} + 180 y = 150 sin (3 t)

y = c_{1} cos (6 t) + c_{2} sin (6 t) + \frac{10}{9} sin (3 t)

Solution steps

5 y^{''} (t) + 180 y = 150 sin (3 t)

Solve linear ODE:

y = c_{1} cos (6 t) + c_{2} sin (6 t) + \frac{10}{9} sin (3 t)

y = c_{1} cos (6 t) + c_{2} sin (6 t) + \frac{10}{9} sin (3 t)

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

y^{^{''}} + 25 y = cos (9 x)

y^{^{''}} - 3 y^{^{'}} + 2 y = \frac{e ^{2 t}}{e ^{2 t} + 1}

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

y^{^{''}} + 4 y = t^{2} + 8 e^{t}

What is the solution for 5y^{''}+180y=150sin(3t) ?
The solution for 5y^{''}+180y=150sin(3t) is y=c_{1}cos(6t)+c_{2}sin(6t)+10/9 sin(3t)