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

The solution for y^{''}+8y^'+16y=0,y(-1)=2,y^'(-1)=2 is y=12e^{-4t-4}+10e^{-4t-4}t

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

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

y = 12 e^{- 4 t - 4} + 10 e^{- 4 t - 4} t

Solution steps

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

Solve linear ODE:

y = 12 e^{- 4 t - 4} + 10 e^{- 4 t - 4} t

y = 12 e^{- 4 t - 4} + 10 e^{- 4 t - 4} t

What is the solution for y^{''}+8y^'+16y=0,y(-1)=2,y^'(-1)=2 ?
The solution for y^{''}+8y^'+16y=0,y(-1)=2,y^'(-1)=2 is y=12e^{-4t-4}+10e^{-4t-4}t