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

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

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(d^2y)/(dx^2)+2(dy)/(dx)+y=e^{-2x}

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} + y = e^{- 2 x}

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} + y = e^{- 2 x}

Solve linear ODE:

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

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

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