What is the solution for y^{'''}+3y^{''}+3y^'+y=0 ?

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

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

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

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

Solution steps

y^{'''} (t) + 3 y^{''} (t) + 3 y^{'} (t) + y = 0

Solve linear ODE:

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

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

\frac{\partial}{\partial x} (\frac{5 y}{x ^{3}})

y^{^{''}} - 9 y^{^{'}} + 18 y = 5 sin (4 t), y (0) = 5, y^{^{'}} (0) = 2

x e^{- 3 x}

\int e^{x} 81 - e^{2 x} d x

y^{^{'}} - y = 3 t e^{2 t}

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