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

The solution for (d^2y)/(dx^2)-(dy)/(dx)-2y=2e^{-x} is y=c_{1}e^{2x}+c_{2}e^{-x}-(2e^{-x}x)/3

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

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

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

Solution steps

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

Solve linear ODE:

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

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

3 x^{^{''}} + 3 x = 5 cos (4 t)

y^{^{''}} + \frac{1}{8} y^{^{'}} + y = 3 \cdot cos (x)

y^{^{''}} + 5 y^{^{'}} - 6 y = 21 e^{t}

y^{^{''''}} + 2 y^{^{''}} + y = cos (2 x) + 2

y^{^{''}} - 2 y^{^{'}} + 5 y = 10 sin (x)

What is the solution for (d^2y)/(dx^2)-(dy)/(dx)-2y=2e^{-x} ?
The solution for (d^2y)/(dx^2)-(dy)/(dx)-2y=2e^{-x} is y=c_{1}e^{2x}+c_{2}e^{-x}-(2e^{-x}x)/3