What is the solution for y^{''}-y^'-2y=2e^{-t} ?

The solution for y^{''}-y^'-2y=2e^{-t} is y=c_{1}e^{2t}+c_{2}e^{-t}-(2e^{-t}t)/3

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y^{''}-y^'-2y=2e^{-t}

y^{^{''}} - y^{^{'}} - 2 y = 2 e^{- t}

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

Solution steps

y^{''} (t) - y^{'} (t) - 2 y = 2 e^{- t}

Solve linear ODE:

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

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

\int tan^{3} (x) sec^{\frac{1}{2}} (x) d x

x \to 0 lim (\frac{1}{e ^{x}})

x \to 6 lim (\frac{x}{x ^{2} - 36})

\frac{d x}{d t} + x = - e^{t}

\frac{d}{d x} ((3 t^{2} - t + a^{2})^{101})

What is the solution for y^{''}-y^'-2y=2e^{-t} ?
The solution for y^{''}-y^'-2y=2e^{-t} is y=c_{1}e^{2t}+c_{2}e^{-t}-(2e^{-t}t)/3