What is the solution for y^{''}+12y^'+27y=64e^{-1t},y(0)=5 ?

The solution for y^{''}+12y^'+27y=64e^{-1t},y(0)=5 is y=(-c_{2}+1)e^{-3t}+c_{2}e^{-9t}+4e^{-t}

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y^{''}+12y^'+27y=64e^{-1t},y(0)=5

y^{^{''}} + 12 y^{^{'}} + 27 y = 64 e^{- 1 t}, y (0) = 5

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

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

y^{^{''}} - y = e^{t} sin (t)

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

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

y^{^{''}} - 2 y^{^{'}} + y = e^{x} (x^{2} - x + 1)

y^{^{''}} - 2 y^{^{'}} + y = e^{x} \frac{1}{x}

What is the solution for y^{''}+12y^'+27y=64e^{-1t},y(0)=5 ?
The solution for y^{''}+12y^'+27y=64e^{-1t},y(0)=5 is y=(-c_{2}+1)e^{-3t}+c_{2}e^{-9t}+4e^{-t}