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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{'''}} - 7 y^{^{'}} + 6 y = 0

16 y^{^{''''}} + 24 y^{^{''}} + 9 y = 0

y^{^{''}} - 4 y^{^{'}} = 0, y (0) = 1, y^{^{'}} (0) = 1

(d^{3} - 3 d^{2} + 4) y = 0

10 y^{^{''}} - 32 y^{^{'}} + 25.6 y = 0

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