What is the solution for y^{'''}+4y^{''}+5y^'+2y=0 ?

The solution for y^{'''}+4y^{''}+5y^'+2y=0 is y=c_{1}e^{-2t}+c_{2}e^{-t}+c_{3}te^{-t}

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y^{'''}+4y^{''}+5y^'+2y=0

y^{^{'''}} + 4 y^{^{''}} + 5 y^{^{'}} + 2 y = 0

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

Solution steps

y^{'''} (t) + 4 y^{''} (t) + 5 y^{'} (t) + 2 y = 0

Solve linear ODE:

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

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

What is the solution for y^{'''}+4y^{''}+5y^'+2y=0 ?
The solution for y^{'''}+4y^{''}+5y^'+2y=0 is y=c_{1}e^{-2t}+c_{2}e^{-t}+c_{3}te^{-t}