What is the solution for y^{''}+4y^'+4y=0,y(-1)=2,y^'(-1)=1 ?

The solution for y^{''}+4y^'+4y=0,y(-1)=2,y^'(-1)=1 is y=7e^{-2t-2}+5e^{-2t-2}t

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y^{''}+4y^'+4y=0,y(-1)=2,y^'(-1)=1

y^{^{''}} + 4 y^{^{'}} + 4 y = 0, y (- 1) = 2, y^{^{'}} (- 1) = 1

y = 7 e^{- 2 t - 2} + 5 e^{- 2 t - 2} t

Solution steps

y^{''} (t) + 4 y^{'} (t) + 4 y = 0

Solve linear ODE:

y = 7 e^{- 2 t - 2} + 5 e^{- 2 t - 2} t

y = 7 e^{- 2 t - 2} + 5 e^{- 2 t - 2} t

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What is the solution for y^{''}+4y^'+4y=0,y(-1)=2,y^'(-1)=1 ?
The solution for y^{''}+4y^'+4y=0,y(-1)=2,y^'(-1)=1 is y=7e^{-2t-2}+5e^{-2t-2}t