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

The solution for y^{''}+4y^'+4y=0,y(-1)=5,y^'(-1)=4 is y=19e^{-2t-2}+14e^{-2t-2}t

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

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

y = 19 e^{- 2 t - 2} + 14 e^{- 2 t - 2} t

Solution steps

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

Solve linear ODE:

y = 19 e^{- 2 t - 2} + 14 e^{- 2 t - 2} t

y = 19 e^{- 2 t - 2} + 14 e^{- 2 t - 2} t

r^{^{''}} - 4 r^{^{'}} - 53 r = 0

(D^{3} + 2 D^{2} + D + 2) y = 0

y^{^{''''}} - 4 y^{^{'''}} + 2 y^{^{''}} + 4 y^{^{'}} - 3 y = 0

y^{^{''''}} + y^{^{'''}} - 2 y^{^{''}} = 0

y^{^{'''}} - 6 y^{^{'}} + 11 y^{^{'}} - 6 y = 0

What is the solution for y^{''}+4y^'+4y=0,y(-1)=5,y^'(-1)=4 ?
The solution for y^{''}+4y^'+4y=0,y(-1)=5,y^'(-1)=4 is y=19e^{-2t-2}+14e^{-2t-2}t