What is the solution for y^{''}+2y^'-2y=8e^{-3x} ?

The solution for y^{''}+2y^'-2y=8e^{-3x} is y=c_{1}e^{(-1+sqrt(3))x}+c_{2}e^{(-1-sqrt(3))x}+8e^{-3x}

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y^{''}+2y^'-2y=8e^{-3x}

y^{^{''}} + 2 y^{^{'}} - 2 y = 8 e^{- 3 x}

y = c_{1} e^{(- 1 + 3) x} + c_{2} e^{(- 1 - 3) x} + 8 e^{- 3 x}

Solution steps

y^{''} (x) + 2 y^{'} (x) - 2 y = 8 e^{- 3 x}

Solve linear ODE:

y = c_{1} e^{(- 1 + 3) x} + c_{2} e^{(- 1 - 3) x} + 8 e^{- 3 x}

y = c_{1} e^{(- 1 + 3) x} + c_{2} e^{(- 1 - 3) x} + 8 e^{- 3 x}

What is the solution for y^{''}+2y^'-2y=8e^{-3x} ?
The solution for y^{''}+2y^'-2y=8e^{-3x} is y=c_{1}e^{(-1+sqrt(3))x}+c_{2}e^{(-1-sqrt(3))x}+8e^{-3x}