What is the solution for linear (d^2y)/(dx^2)+4((dy)/(dx))+4y=0 ?

The solution for linear (d^2y)/(dx^2)+4((dy)/(dx))+4y=0 is y=c_{1}e^{-2x}+c_{2}xe^{-2x}

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linear (d^2y)/(dx^2)+4((dy)/(dx))+4y=0

linear

\frac{d ^{2} y}{d x ^{2}} + 4 (\frac{d y}{d x}) + 4 y = 0

y = c_{1} e^{- 2 x} + c_{2} x e^{- 2 x}

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 4 (\frac{d y}{d x}) + 4 y = 0

Solve linear ODE:

y = c_{1} e^{- 2 x} + c_{2} x e^{- 2 x}

y = c_{1} e^{- 2 x} + c_{2} x e^{- 2 x}

4 x^{^{''}} + 3 x^{^{'}} + 5 x = 0

y^{^{''}} + 64 y = 0, y^{^{'}} (0) = 0

x^{^{''}} + 2^{2} \cdot 3^{2} x = 0

y^{^{''}} + 4 y = 0, y (0) = \frac{1}{2}, y^{^{'}} (0) = 3

y^{^{'''}} - y^{^{''}} - 12 y^{^{'}} - 40 y = 0, y (0) = e^{5 x}

What is the solution for linear (d^2y)/(dx^2)+4((dy)/(dx))+4y=0 ?
The solution for linear (d^2y)/(dx^2)+4((dy)/(dx))+4y=0 is y=c_{1}e^{-2x}+c_{2}xe^{-2x}