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

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

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y^{'''}+y^{''}=e^t+t+1

y^{^{'''}} + y^{^{''}} = e^{t} + t + 1

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

Solution steps

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

Solve linear ODE:

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

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

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