What is the solution for y^{''}+4y^'+4y=0,y(0)=11 ?

The solution for y^{''}+4y^'+4y=0,y(0)=11 is y=11e^{-2t}+c_{2}te^{-2t}

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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