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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

\frac{\partial}{\partial x} (2^{\frac{1}{x}})

(3, 5), (8, 7)

\int \frac{3 x ^{2} - 6 x ^{2} + x}{x ^{3}} d x

y = 5 x + 20, at x = 1

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