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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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