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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

2500 y^{^{''}} + 81 y = 0

y^{^{''}} + 5 y^{^{'}} - 24 y = 0, y (0) = x, y^{^{'}} (0) = 56

y^{^{''}} - 9 y = 0, y (0) = 1, y^{^{'}} (0) = - 1

\frac{d ^{2} y}{d t ^{2}} + 4 y = 0

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} - 6 y = 0

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