What is the solution for -y^{'''}+2y^{''}+3y^'+3=0 ?

The solution for -y^{'''}+2y^{''}+3y^'+3=0 is y=c_{1}+c_{2}e^{-t}+c_{3}e^{3t}-t

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-y^{'''}+2y^{''}+3y^'+3=0

- y^{^{'''}} + 2 y^{^{''}} + 3 y^{^{'}} + 3 = 0

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

Solution steps

- y^{'''} (t) + 2 y^{''} (t) + 3 y^{'} (t) + 3 = 0

Solve linear ODE:

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

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

What is the solution for -y^{'''}+2y^{''}+3y^'+3=0 ?
The solution for -y^{'''}+2y^{''}+3y^'+3=0 is y=c_{1}+c_{2}e^{-t}+c_{3}e^{3t}-t