What is the solution for y^{''}+2y^'+y=0,y(0)=5,y(0)=-3 ?

The solution for y^{''}+2y^'+y=0,y(0)=5,y(0)=-3 is y=5e^{-t}+c_{2}te^{-t}

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y^{''}+2y^'+y=0,y(0)=5,y(0)=-3

y^{^{''}} + 2 y^{^{'}} + y = 0, y (0) = 5, y (0) = - 3

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

Solution steps

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

Solve linear ODE:

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

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

What is the solution for y^{''}+2y^'+y=0,y(0)=5,y(0)=-3 ?
The solution for y^{''}+2y^'+y=0,y(0)=5,y(0)=-3 is y=5e^{-t}+c_{2}te^{-t}