What is the solution for y^{''}-16y^'+64y=504sin(x)-128cos(x) ?

The solution for y^{''}-16y^'+64y=504sin(x)-128cos(x) is y=c_{1}e^{8x}+c_{2}xe^{8x}+8sin(x)

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y^{''}-16y^'+64y=504sin(x)-128cos(x)

y^{^{''}} - 16 y^{^{'}} + 64 y = 504 sin (x) - 128 cos (x)

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

Solution steps

y^{''} (x) - 16 y^{'} (x) + 64 y = 504 sin (x) - 128 cos (x)

Solve linear ODE:

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

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

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

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

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

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

4 y^{^{''}} - 4 y^{^{'}} + y = 40 e^{\frac{t}{2}}

What is the solution for y^{''}-16y^'+64y=504sin(x)-128cos(x) ?
The solution for y^{''}-16y^'+64y=504sin(x)-128cos(x) is y=c_{1}e^{8x}+c_{2}xe^{8x}+8sin(x)