What is the solution for y^{''}+2y^'+y=0,y(0)=-1,y^'(0)=-3 ?

The solution for y^{''}+2y^'+y=0,y(0)=-1,y^'(0)=-3 is y=-e^{-t}-4e^{-t}t

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y^{''}+2y^'+y=0,y(0)=-1,y^'(0)=-3

y^{^{''}} + 2 y^{^{'}} + y = 0, y (0) = - 1, y^{^{'}} (0) = - 3

y = - e^{- t} - 4 e^{- t} t

Solution steps

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

Solve linear ODE:

y = - e^{- t} - 4 e^{- t} t

y = - e^{- t} - 4 e^{- t} t

What is the solution for y^{''}+2y^'+y=0,y(0)=-1,y^'(0)=-3 ?
The solution for y^{''}+2y^'+y=0,y(0)=-1,y^'(0)=-3 is y=-e^{-t}-4e^{-t}t