What is the solution for y^{'''}+14y^{''}+49y^'=0 ?

The solution for y^{'''}+14y^{''}+49y^'=0 is y=c_{1}+c_{2}e^{-7t}+c_{3}te^{-7t}

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y^{'''}+14y^{''}+49y^'=0

y^{^{'''}} + 14 y^{^{''}} + 49 y^{^{'}} = 0

y = c_{1} + c_{2} e^{- 7 t} + c_{3} t e^{- 7 t}

Solution steps

y^{'''} (t) + 14 y^{''} (t) + 49 y^{'} (t) = 0

Solve linear ODE:

y = c_{1} + c_{2} e^{- 7 t} + c_{3} t e^{- 7 t}

y = c_{1} + c_{2} e^{- 7 t} + c_{3} t e^{- 7 t}

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What is the solution for y^{'''}+14y^{''}+49y^'=0 ?
The solution for y^{'''}+14y^{''}+49y^'=0 is y=c_{1}+c_{2}e^{-7t}+c_{3}te^{-7t}