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

The solution for y^{''}+8y^'+16y=x is y=c_{1}e^{-4x}+c_{2}xe^{-4x}+x/(16)-1/32

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y^{''}+8y^'+16y=x

y^{^{''}} + 8 y^{^{'}} + 16 y = x

y = c_{1} e^{- 4 x} + c_{2} x e^{- 4 x} + \frac{x}{16} - \frac{1}{32}

Solution steps

y^{''} (x) + 8 y^{'} (x) + 16 y = x

Solve linear ODE:

y = c_{1} e^{- 4 x} + c_{2} x e^{- 4 x} + \frac{x}{16} - \frac{1}{32}

y = c_{1} e^{- 4 x} + c_{2} x e^{- 4 x} + \frac{x}{16} - \frac{1}{32}

What is the solution for y^{''}+8y^'+16y=x ?
The solution for y^{''}+8y^'+16y=x is y=c_{1}e^{-4x}+c_{2}xe^{-4x}+x/(16)-1/32