What is the solution for y^{''}+36y=24sin(6x) ?

The solution for y^{''}+36y=24sin(6x) is y=c_{1}cos(6x)+c_{2}sin(6x)-2xcos(6x)

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y^{''}+36y=24sin(6x)

y^{^{''}} + 36 y = 24 sin (6 x)

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

Solution steps

y^{''} (x) + 36 y = 24 sin (6 x)

Solve linear ODE:

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

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

y^{^{''}} + 6 y = g (t)

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

2 x^{^{''}} + 5 x^{^{'}} + 2 x = 2 e - 2 t - t

y^{^{''}} + 5 y^{^{'}} + 6 y = t e^{t}

x^{^{''}} + 2^{2} \cdot x = 3 \cdot cos (b t)

What is the solution for y^{''}+36y=24sin(6x) ?
The solution for y^{''}+36y=24sin(6x) is y=c_{1}cos(6x)+c_{2}sin(6x)-2xcos(6x)