What is the solution for (d^2y)/(dx^2)+8(dy)/(dx)+16y=e^{4x} ?

The solution for (d^2y)/(dx^2)+8(dy)/(dx)+16y=e^{4x} is y=c_{1}e^{-4x}+c_{2}xe^{-4x}+1/64 e^{4x}

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(d^2y)/(dx^2)+8(dy)/(dx)+16y=e^{4x}

\frac{d ^{2} y}{d x ^{2}} + 8 \frac{d y}{d x} + 16 y = e^{4 x}

y = c_{1} e^{- 4 x} + c_{2} x e^{- 4 x} + \frac{1}{64} e^{4 x}

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 8 \frac{d y}{d x} + 16 y = e^{4 x}

Solve linear ODE:

y = c_{1} e^{- 4 x} + c_{2} x e^{- 4 x} + \frac{1}{64} e^{4 x}

y = c_{1} e^{- 4 x} + c_{2} x e^{- 4 x} + \frac{1}{64} e^{4 x}

What is the solution for (d^2y)/(dx^2)+8(dy)/(dx)+16y=e^{4x} ?
The solution for (d^2y)/(dx^2)+8(dy)/(dx)+16y=e^{4x} is y=c_{1}e^{-4x}+c_{2}xe^{-4x}+1/64 e^{4x}