What is the solution for y^{''}-3y^'-28y=528e^{-t} ?

The solution for y^{''}-3y^'-28y=528e^{-t} is y=c_{1}e^{7t}+c_{2}e^{-4t}-22e^{-t}

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y^{''}-3y^'-28y=528e^{-t}

y^{^{''}} - 3 y^{^{'}} - 28 y = 528 e^{- t}

y = c_{1} e^{7 t} + c_{2} e^{- 4 t} - 22 e^{- t}

Solution steps

y^{''} (t) - 3 y^{'} (t) - 28 y = 528 e^{- t}

Solve linear ODE:

y = c_{1} e^{7 t} + c_{2} e^{- 4 t} - 22 e^{- t}

y = c_{1} e^{7 t} + c_{2} e^{- 4 t} - 22 e^{- t}

y^{^{''}} + y^{^{'}} + y = e^{3 x} + 6 e^{x} - 3 e^{- 2 x} + 5

d (x) = 5 (x - 3)^{2} + 1

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

y^{^{''}} + y^{^{'}} - 2 y = 4

y^{^{''}} + y = 1, y (0) = 6, y^{^{'}} (0) = 0

What is the solution for y^{''}-3y^'-28y=528e^{-t} ?
The solution for y^{''}-3y^'-28y=528e^{-t} is y=c_{1}e^{7t}+c_{2}e^{-4t}-22e^{-t}