What is the solution for y^{''}+5y^'+6y=1+e^{-t} ?

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

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y^{''}+5y^'+6y=1+e^{-t}

y^{^{''}} + 5 y^{^{'}} + 6 y = 1 + e^{- t}

y = c_{1} e^{- 2 t} + c_{2} e^{- 3 t} + \frac{1}{6} + \frac{1}{2} e^{- t}

Solution steps

y^{''} (t) + 5 y^{'} (t) + 6 y = 1 + e^{- t}

Solve linear ODE:

y = c_{1} e^{- 2 t} + c_{2} e^{- 3 t} + \frac{1}{6} + \frac{1}{2} e^{- t}

y = c_{1} e^{- 2 t} + c_{2} e^{- 3 t} + \frac{1}{6} + \frac{1}{2} e^{- t}

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