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

The solution for y^{''}+2αy^'+α^2y=0 is y=c_{1}e^{-αt}+c_{2}te^{-αt}

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y^{''}+2αy^'+α^2y=0

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

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

Solution steps

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

Solve linear ODE:

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

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

What is the solution for y^{''}+2αy^'+α^2y=0 ?
The solution for y^{''}+2αy^'+α^2y=0 is y=c_{1}e^{-αt}+c_{2}te^{-αt}