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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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