What is the solution for y^{''}+8y^'+16y=0,y(-1)=5,y^'(-1)=2 ?

The solution for y^{''}+8y^'+16y=0,y(-1)=5,y^'(-1)=2 is y=27e^{-4t-4}+22e^{-4t-4}t

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y^{''}+8y^'+16y=0,y(-1)=5,y^'(-1)=2

y^{^{''}} + 8 y^{^{'}} + 16 y = 0, y (- 1) = 5, y^{^{'}} (- 1) = 2

y = 27 e^{- 4 t - 4} + 22 e^{- 4 t - 4} t

Solution steps

y^{''} (t) + 8 y^{'} (t) + 16 y = 0

Solve linear ODE:

y = 27 e^{- 4 t - 4} + 22 e^{- 4 t - 4} t

y = 27 e^{- 4 t - 4} + 22 e^{- 4 t - 4} t

c y^{^{''}} + ab y^{^{'}} = 0, y (0) = 1, y (1.2) = 0

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

y^{^{''}} + 2 y^{^{'}} + 65 y = 0, y (0) = - 1, y^{^{'}} (0) = 33

y^{^{''}} - 4 y^{^{'}} + 13 y = 0, y (0) = - 5

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

What is the solution for y^{''}+8y^'+16y=0,y(-1)=5,y^'(-1)=2 ?
The solution for y^{''}+8y^'+16y=0,y(-1)=5,y^'(-1)=2 is y=27e^{-4t-4}+22e^{-4t-4}t