What is the solution for y^{''}+16y=cos(4x) ?

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

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y^{''}+16y=cos(4x)

y^{^{''}} + 16 y = cos (4 x)

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

Solution steps

y^{''} (x) + 16 y = cos (4 x)

Solve linear ODE:

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

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

y^{^{''}} - 5 y^{^{'}} - 36 y = x - 8

y^{^{''}} - y^{^{'}} = t e^{t}

x^{^{''}} - x = e^{t} sin (e^{- t}) cos (e^{- t})

y^{^{''}} + y^{^{'}} - 20 y = 4 e^{2} t

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

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