What is the solution for y^{''}+16y^'+64y=100e^{2x} ?

The solution for y^{''}+16y^'+64y=100e^{2x} is y=c_{1}e^{-8x}+c_{2}xe^{-8x}+e^{2x}

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y^{''}+16y^'+64y=100e^{2x}

y^{^{''}} + 16 y^{^{'}} + 64 y = 100 e^{2 x}

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

Solution steps

y^{''} (x) + 16 y^{'} (x) + 64 y = 100 e^{2 x}

Solve linear ODE:

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

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

2 y^{^{''}} - 5 y^{^{'}} + 71.86 y = 4

y^{^{''}} - 2 y^{^{'}} - 3 y = 6 x e^{x} + 4 x - 5

y^{^{''}} - 2 y^{^{'}} + 5 y = cos (x)

y^{^{''}} + 3 y = 5 t^{4}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} - 10 y^{^{'}} + 24 = 0

What is the solution for y^{''}+16y^'+64y=100e^{2x} ?
The solution for y^{''}+16y^'+64y=100e^{2x} is y=c_{1}e^{-8x}+c_{2}xe^{-8x}+e^{2x}