What is the solution for y^{''}-4y^'-5y=3e^{-4t} ?

The solution for y^{''}-4y^'-5y=3e^{-4t} is y=c_{1}e^{5t}+c_{2}e^{-t}+1/9 e^{-4t}

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y^{''}-4y^'-5y=3e^{-4t}

y^{^{''}} - 4 y^{^{'}} - 5 y = 3 e^{- 4 t}

y = c_{1} e^{5 t} + c_{2} e^{- t} + \frac{1}{9} e^{- 4 t}

Solution steps

y^{''} (t) - 4 y^{'} (t) - 5 y = 3 e^{- 4 t}

Solve linear ODE:

y = c_{1} e^{5 t} + c_{2} e^{- t} + \frac{1}{9} e^{- 4 t}

y = c_{1} e^{5 t} + c_{2} e^{- t} + \frac{1}{9} e^{- 4 t}

y^{^{''}} + 4 y = 6 cos (2 t), y (0) = 2, y^{^{'}} (0) = 1

y^{^{''}} - 9 y = - 27 t + 18 t^{2}

y^{^{'''}} - 2 y^{^{''}} + 26 y^{^{'}} = 174 e^{3 x}

y^{^{''}} + y^{^{'}} - y = t^{3}, y (0) = 1, y^{^{'}} (0) = 0

- y^{^{''}} + 2 y^{^{'}} + 3 y = 1, y (0) = 0, y (1) = (0)

What is the solution for y^{''}-4y^'-5y=3e^{-4t} ?
The solution for y^{''}-4y^'-5y=3e^{-4t} is y=c_{1}e^{5t}+c_{2}e^{-t}+1/9 e^{-4t}