What is the solution for y^{''}+12y^'+27y=64e^{-1t} ?

The solution for y^{''}+12y^'+27y=64e^{-1t} is y=c_{1}e^{-3t}+c_{2}e^{-9t}+4e^{-t}

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y^{''}+12y^'+27y=64e^{-1t}

y^{^{''}} + 12 y^{^{'}} + 27 y = 64 e^{- 1 t}

y = c_{1} e^{- 3 t} + c_{2} e^{- 9 t} + 4 e^{- t}

Solution steps

y^{''} (t) + 12 y^{'} (t) + 27 y = 64 e^{- 1 t}

Solve linear ODE:

y = c_{1} e^{- 3 t} + c_{2} e^{- 9 t} + 4 e^{- t}

y = c_{1} e^{- 3 t} + c_{2} e^{- 9 t} + 4 e^{- t}

y^{^{''}} + 4 y = 4 \cdot sec^{2} (2 t)

2 y^{^{''}} - 6 y^{^{'}} = 5, y (0) = 2, y^{^{'}} (0) = 1

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

y^{^{''}} + 5 y^{^{'}} + 6 y = 1, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} + 25 y = 17 sec^{2} (5 t)

What is the solution for y^{''}+12y^'+27y=64e^{-1t} ?
The solution for y^{''}+12y^'+27y=64e^{-1t} is y=c_{1}e^{-3t}+c_{2}e^{-9t}+4e^{-t}