What is the solution for y^{''}+9y^'+8y=e^{2t} ?

The solution for y^{''}+9y^'+8y=e^{2t} is y=c_{1}e^{-t}+c_{2}e^{-8t}+1/30 e^{2t}

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y^{''}+9y^'+8y=e^{2t}

y^{^{''}} + 9 y^{^{'}} + 8 y = e^{2 t}

y = c_{1} e^{- t} + c_{2} e^{- 8 t} + \frac{1}{30} e^{2 t}

Solution steps

y^{''} (t) + 9 y^{'} (t) + 8 y = e^{2 t}

Solve linear ODE:

y = c_{1} e^{- t} + c_{2} e^{- 8 t} + \frac{1}{30} e^{2 t}

y = c_{1} e^{- t} + c_{2} e^{- 8 t} + \frac{1}{30} e^{2 t}

y^{^{'''}} + 7 y^{^{''}} + 8 y^{^{'}} - 16 y = - 3 e^{x} - 2

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

y^{^{''}} + y^{^{'}} - 6 y = 2 t

y^{^{'''}} - 5 y^{^{''}} + 6 y^{^{'}} = 8 + 2 sin (x)

y^{^{''}} + y = 3 sin (2 t) + t cos (2 t)

What is the solution for y^{''}+9y^'+8y=e^{2t} ?
The solution for y^{''}+9y^'+8y=e^{2t} is y=c_{1}e^{-t}+c_{2}e^{-8t}+1/30 e^{2t}