What is the solution for y^{''}+y=5sin(4x) ?

The solution for y^{''}+y=5sin(4x) is y=c_{1}cos(x)+c_{2}sin(x)-1/3 sin(4x)

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y^{''}+y=5sin(4x)

y^{^{''}} + y = 5 sin (4 x)

y = c_{1} cos (x) + c_{2} sin (x) - \frac{1}{3} sin (4 x)

Solution steps

y^{''} (x) + y = 5 sin (4 x)

Solve linear ODE:

y = c_{1} cos (x) + c_{2} sin (x) - \frac{1}{3} sin (4 x)

y = c_{1} cos (x) + c_{2} sin (x) - \frac{1}{3} sin (4 x)

12 y^{^{''}} + 5 y^{^{'}} - 3 y = e^{x}

y^{^{''}} - 3 y^{^{'}} - 2 y = 9 e^{- x}

(D^{3} + D^{2} + 5 D + 5) y = 5 cos (2 x)

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

y^{^{''}} - 2 y^{^{'}} - 3 y = 32 e^{- x}

What is the solution for y^{''}+y=5sin(4x) ?
The solution for y^{''}+y=5sin(4x) is y=c_{1}cos(x)+c_{2}sin(x)-1/3 sin(4x)