What is the solution for y^{''}+16y=sin(8x) ?

The solution for y^{''}+16y=sin(8x) is y=c_{1}cos(4x)+c_{2}sin(4x)-1/48 sin(8x)

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y^{''}+16y=sin(8x)

y^{^{''}} + 16 y = sin (8 x)

y = c_{1} cos (4 x) + c_{2} sin (4 x) - \frac{1}{48} sin (8 x)

Solution steps

y^{''} (x) + 16 y = sin (8 x)

Solve linear ODE:

y = c_{1} cos (4 x) + c_{2} sin (4 x) - \frac{1}{48} sin (8 x)

y = c_{1} cos (4 x) + c_{2} sin (4 x) - \frac{1}{48} sin (8 x)

2 x^{^{''}} + 3 x^{^{'}} + 5 x = 2 t

y^{^{''}} - 6 y^{^{'}} + 8 y = 8 e^{4 x}

2 y^{^{''}} + 18 y = 3 tan (3 x)

y^{^{''}} + y = e^{- 2 t} sin (t), y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 4 y^{^{'}} + 4 y = x^{3} e^{2 x}

What is the solution for y^{''}+16y=sin(8x) ?
The solution for y^{''}+16y=sin(8x) is y=c_{1}cos(4x)+c_{2}sin(4x)-1/48 sin(8x)