What is the solution for y^{''}+y^'-20y=3e^t ?

The solution for y^{''}+y^'-20y=3e^t is y=c_{1}e^{4t}+c_{2}e^{-5t}-1/6 e^t

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y^{''}+y^'-20y=3e^t

y^{^{''}} + y^{^{'}} - 20 y = 3 e^{t}

y = c_{1} e^{4 t} + c_{2} e^{- 5 t} - \frac{1}{6} e^{t}

Solution steps

y^{''} (t) + y^{'} (t) - 20 y = 3 e^{t}

Solve linear ODE:

y = c_{1} e^{4 t} + c_{2} e^{- 5 t} - \frac{1}{6} e^{t}

y = c_{1} e^{4 t} + c_{2} e^{- 5 t} - \frac{1}{6} e^{t}

What is the solution for y^{''}+y^'-20y=3e^t ?
The solution for y^{''}+y^'-20y=3e^t is y=c_{1}e^{4t}+c_{2}e^{-5t}-1/6 e^t