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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + 2 y^{^{'}} + y = 2 x

x^{^{''}} + 8 x^{^{'}} + 16 x = 4 sin (4 t)

y^{^{''}} - 6 y^{^{'}} + 9 y = t, y (0) = 0, y (0) = 1

y^{^{''}} - 2 y^{^{'}} - 3 y = 3 x - 4

y^{^{''}} + 2 y^{^{'}} = 2 x + 5 + e^{- 2 x}

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