What is the solution for y^{'''}-3y^'+2y=e^{-2x} ?

The solution for y^{'''}-3y^'+2y=e^{-2x} is y=c_{1}e^{-2x}+c_{2}e^x+c_{3}xe^x+(e^{-2x}x)/9

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

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

y = c_{1} e^{- 2 x} + c_{2} e^{x} + c_{3} x e^{x} + \frac{e ^{- 2 x} x}{9}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{- 2 x} + c_{2} e^{x} + c_{3} x e^{x} + \frac{e ^{- 2 x} x}{9}

y = c_{1} e^{- 2 x} + c_{2} e^{x} + c_{3} x e^{x} + \frac{e ^{- 2 x} x}{9}

What is the solution for y^{'''}-3y^'+2y=e^{-2x} ?
The solution for y^{'''}-3y^'+2y=e^{-2x} is y=c_{1}e^{-2x}+c_{2}e^x+c_{3}xe^x+(e^{-2x}x)/9