What is the solution for y^{''}+4y^'+4y=0,y(-1)=3,y^'(-1)=5 ?

The solution for y^{''}+4y^'+4y=0,y(-1)=3,y^'(-1)=5 is y=14e^{-2t-2}+11e^{-2t-2}t

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y^{''}+4y^'+4y=0,y(-1)=3,y^'(-1)=5

y^{^{''}} + 4 y^{^{'}} + 4 y = 0, y (- 1) = 3, y^{^{'}} (- 1) = 5

y = 14 e^{- 2 t - 2} + 11 e^{- 2 t - 2} t

Solution steps

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

Solve linear ODE:

y = 14 e^{- 2 t - 2} + 11 e^{- 2 t - 2} t

y = 14 e^{- 2 t - 2} + 11 e^{- 2 t - 2} t

y^{^{''}} + y^{^{'}} + 11 y = 0, y^{^{'}} (0) = 1, y (0) = 4

y^{^{''}} + 2 y^{^{'}} - 8 y = 0, y (0) = 3

S^{^{''}} + 16 S = 0, S (0) = 4, S^{^{'}} (0) = 2

y^{^{''}} - y^{^{'}} - 20 y = 0, y (0) = α, y^{^{'}} (0) = 2

144 y^{^{''}} - 312 y^{^{'}} + 169 y = 0

What is the solution for y^{''}+4y^'+4y=0,y(-1)=3,y^'(-1)=5 ?
The solution for y^{''}+4y^'+4y=0,y(-1)=3,y^'(-1)=5 is y=14e^{-2t-2}+11e^{-2t-2}t