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

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

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

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

y = c_{1} + c_{2} t + c_{3} e^{- t} + c_{4} t e^{- t}

Solution steps

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

Solve linear ODE:

y = c_{1} + c_{2} t + c_{3} e^{- t} + c_{4} t e^{- t}

y = c_{1} + c_{2} t + c_{3} e^{- t} + c_{4} t e^{- t}

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