What is the solution for y^{''}-16y^'+64y=2e^{8x} ?

The solution for y^{''}-16y^'+64y=2e^{8x} is y=c_{1}e^{8x}+c_{2}xe^{8x}+e^{8x}x^2

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y^{''}-16y^'+64y=2e^{8x}

y^{^{''}} - 16 y^{^{'}} + 64 y = 2 e^{8 x}

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

Solution steps

y^{''} (x) - 16 y^{'} (x) + 64 y = 2 e^{8 x}

Solve linear ODE:

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

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

y^{^{''}} + 9 y = 9 sec (3 t)

y^{^{''}} - y^{^{'}} + 81 y = 9 sin (9 t)

y^{^{''}} + 4 y = 16 t, y^{0} = 3, y^{^{'}} 0 = - 6

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

y^{^{''}} - 7 y = t^{2}

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