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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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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