What is the solution for y^{''}-y^'-2y=4e^{-t} ?

The solution for y^{''}-y^'-2y=4e^{-t} is y=c_{1}e^{2t}+c_{2}e^{-t}-(4e^{-t}t)/3

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y^{''}-y^'-2y=4e^{-t}

y^{^{''}} - y^{^{'}} - 2 y = 4 e^{- t}

y = c_{1} e^{2 t} + c_{2} e^{- t} - \frac{4 e ^{- t} t}{3}

Solution steps

y^{''} (t) - y^{'} (t) - 2 y = 4 e^{- t}

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} e^{- t} - \frac{4 e ^{- t} t}{3}

y = c_{1} e^{2 t} + c_{2} e^{- t} - \frac{4 e ^{- t} t}{3}

f (x) = \frac{2}{x - 7}

\int 8 x e^{- x^{2}} d x

x \to 2 lim (\frac{x + 3}{x - 2})

\frac{d}{d x} (- \frac{2}{3 x ^{3}})

\int \frac{18}{( x - 3 ) ( x ^{2} + 9 )} d x

What is the solution for y^{''}-y^'-2y=4e^{-t} ?
The solution for y^{''}-y^'-2y=4e^{-t} is y=c_{1}e^{2t}+c_{2}e^{-t}-(4e^{-t}t)/3