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

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

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

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

y = 2 e^{- 2 t} + 8 t e^{- 2 t}

Solution steps

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

Solve linear ODE:

y = 2 e^{- 2 t} + 8 t e^{- 2 t}

y = 2 e^{- 2 t} + 8 t e^{- 2 t}

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