What is the solution for y^{''}+8y^'=-256cos(8x) ?

The solution for y^{''}+8y^'=-256cos(8x) is y=c_{1}+c_{2}e^{-8x}-2sin(8x)+2cos(8x)

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y^{''}+8y^'=-256cos(8x)

y^{^{''}} + 8 y^{^{'}} = - 256 cos (8 x)

y = c_{1} + c_{2} e^{- 8 x} - 2 sin (8 x) + 2 cos (8 x)

Solution steps

y^{''} (x) + 8 y^{'} (x) = - 256 cos (8 x)

Solve linear ODE:

y = c_{1} + c_{2} e^{- 8 x} - 2 sin (8 x) + 2 cos (8 x)

y = c_{1} + c_{2} e^{- 8 x} - 2 sin (8 x) + 2 cos (8 x)

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