What is the solution for y^{''}-4y=3e-2t ?

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

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y^{''}-4y=3e-2t

y^{^{''}} - 4 y = 3 e - 2 t

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

Solution steps

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

Solve linear ODE:

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

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

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

- y^{^{''}} + y^{^{'}} = 1

y^{^{''''}} - 4 y^{^{''}} = t^{2} - e^{3 t}

y^{^{''}} - 4 y^{^{'}} + 3 y = 4 e^{3 t}, y (0) = 2, y^{^{'}} (0) = 7

\frac{1}{8} y^{^{''}} + 4 y^{^{'}} + 28 x = 0, y (0) = 0, y^{^{'}} (0) = 3

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