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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + 4 y = sin (x), y (0) = 1, y^{^{'}} (0) = 4

x^{^{''}} - x = 3 e^{- 2 t}

y^{^{''''}} - y = 7 t + cos (t)

y^{^{''}} + 3 y^{^{'}} + 2 y = 1, y (0) = 0, y^{^{'}} (0) = 0

y^{^{'''}} - 4 y^{^{'}} = t + 3 cos (t) + e^{- 2 t}

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