What is the solution for y^{''}+256y=20sin(16x) ?

The solution for y^{''}+256y=20sin(16x) is y=c_{1}cos(16x)+c_{2}sin(16x)-(5xcos(16x))/8

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y^{''}+256y=20sin(16x)

y^{^{''}} + 256 y = 20 sin (16 x)

y = c_{1} cos (16 x) + c_{2} sin (16 x) - \frac{5 x cos ( 16 x )}{8}

Solution steps

y^{''} (x) + 256 y = 20 sin (16 x)

Solve linear ODE:

y = c_{1} cos (16 x) + c_{2} sin (16 x) - \frac{5 x cos ( 16 x )}{8}

y = c_{1} cos (16 x) + c_{2} sin (16 x) - \frac{5 x cos ( 16 x )}{8}

2 y^{^{'}} - 3 = - y + y^{^{''}} + 16 e^{3 x} + 3 e^{2 x} + 5

y^{^{''}} + 2 y^{^{'}} - 3 y = 6 x - 3 e^{2 x}

y^{^{''}} + 3 y^{^{'}} + 2 y = sin (t), y (0) = 1, y^{^{'}} (0) = 1

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

y^{^{''}} - 2 y^{^{'}} - 15 y = 3 x

What is the solution for y^{''}+256y=20sin(16x) ?
The solution for y^{''}+256y=20sin(16x) is y=c_{1}cos(16x)+c_{2}sin(16x)-(5xcos(16x))/8