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

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

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

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

y = c_{1} e^{- 5 t} + c_{2} + c_{3} t + c_{4} t^{2}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{- 5 t} + c_{2} + c_{3} t + c_{4} t^{2}

y = c_{1} e^{- 5 t} + c_{2} + c_{3} t + c_{4} t^{2}

4 y^{^{''}} - 68 y^{^{'}} + 289 y = 0

y^{^{''}} + 9 y + y = 0, y (0) = 0.16, y^{^{'}} (0) = 0

y^{^{''}} - 7 y^{^{'}} - 2 y = 0

2 y^{^{''}} + 14 y^{^{'}} + 8 y = 0, y (0) = 5, y^{^{'}} (0) = 0

4 y^{^{''}} + 7 y^{^{'}} + 3 y = 0

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