What is the solution for y^{''}+4y^'+4y=0,y(0)=4,y^'(0)=-6 ?

The solution for y^{''}+4y^'+4y=0,y(0)=4,y^'(0)=-6 is y=4e^{-2t}+2te^{-2t}

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y^{''}+4y^'+4y=0,y(0)=4,y^'(0)=-6

y^{^{''}} + 4 y^{^{'}} + 4 y = 0, y (0) = 4, y^{^{'}} (0) = - 6

y = 4 e^{- 2 t} + 2 t e^{- 2 t}

Solution steps

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

Solve linear ODE:

y = 4 e^{- 2 t} + 2 t e^{- 2 t}

y = 4 e^{- 2 t} + 2 t e^{- 2 t}

y^{^{''}} - 10 y^{^{'}} + 25 y = 0, y (0) = 1, y^{^{'}} (0) = 0

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

y^{^{''}} + 9 y = 0, y^{^{'}} (\frac{π}{2}) = 0, y (0) = 0

y^{^{''}} + y^{^{'}} - 6 y = 0, y (1) = 2 e^{2} - e^{- 3}

(D^{3} - 3 D^{2} + 3 D - 1) y = 0

What is the solution for y^{''}+4y^'+4y=0,y(0)=4,y^'(0)=-6 ?
The solution for y^{''}+4y^'+4y=0,y(0)=4,y^'(0)=-6 is y=4e^{-2t}+2te^{-2t}