What is the solution for y^{''}+2y^'+y=0,y(0)=-1,y^'(0)=-2 ?

The solution for y^{''}+2y^'+y=0,y(0)=-1,y^'(0)=-2 is y=-e^{-t}-3e^{-t}t

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y^{''}+2y^'+y=0,y(0)=-1,y^'(0)=-2

y^{^{''}} + 2 y^{^{'}} + y = 0, y (0) = - 1, y^{^{'}} (0) = - 2

y = - e^{- t} - 3 e^{- t} t

Solution steps

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

Solve linear ODE:

y = - e^{- t} - 3 e^{- t} t

y = - e^{- t} - 3 e^{- t} t

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