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

The solution for y^{''}+3y^'+2y=e^{-x} is y=c_{1}e^{-x}+c_{2}e^{-2x}+e^{-x}x

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

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

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

Solution steps

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

Solve linear ODE:

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

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

x^{^{''}} + 10 x^{^{'}} + 29 x = t e^{- t}

y^{^{'''}} - y^{^{'}} = 9 t

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

y^{^{''}} + 4 y = sin^{2} (2 x)

x^{^{''}} + 36 x = 33 cos (5 t)

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