What is the solution for y^{''}-3y^'-28y=1056e^{-t} ?

The solution for y^{''}-3y^'-28y=1056e^{-t} is y=c_{1}e^{7t}+c_{2}e^{-4t}-44e^{-t}

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y^{''}-3y^'-28y=1056e^{-t}

y^{^{''}} - 3 y^{^{'}} - 28 y = 1056 e^{- t}

y = c_{1} e^{7 t} + c_{2} e^{- 4 t} - 44 e^{- t}

Solution steps

y^{''} (t) - 3 y^{'} (t) - 28 y = 1056 e^{- t}

Solve linear ODE:

y = c_{1} e^{7 t} + c_{2} e^{- 4 t} - 44 e^{- t}

y = c_{1} e^{7 t} + c_{2} e^{- 4 t} - 44 e^{- t}

y^{^{''}} + y = g (t), y (0) = 0, y^{^{'}} (0) = 0

x^{^{''}} - x = 4 e^{- t}

y^{^{''}} + 6 y^{^{'}} + 18 y = 11 t e^{4 t}

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} - 2 y = 8

y^{^{''}} - 10 y^{^{'}} + 25 y = 6 + 3 x

What is the solution for y^{''}-3y^'-28y=1056e^{-t} ?
The solution for y^{''}-3y^'-28y=1056e^{-t} is y=c_{1}e^{7t}+c_{2}e^{-4t}-44e^{-t}