What is the solution for (d^2x)/(dt^2)+8(dx)/(dt)+4x=0 ?

The solution for (d^2x)/(dt^2)+8(dx)/(dt)+4x=0 is x=c_{1}e^{2(sqrt(3)-2)t}+c_{2}e^{-2(2+sqrt(3))t}

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(d^2x)/(dt^2)+8(dx)/(dt)+4x=0

\frac{d ^{2} x}{d t ^{2}} + 8 \frac{d x}{d t} + 4 x = 0

x = c_{1} e^{2 (3 - 2) t} + c_{2} e^{- 2 (2 + 3) t}

Solution steps

\frac{d ^{2} x}{d t ^{2}} + 8 \frac{d x}{d t} + 4 x = 0

Solve linear ODE:

x = c_{1} e^{2 (3 - 2) t} + c_{2} e^{- 2 (2 + 3) t}

x = c_{1} e^{2 (3 - 2) t} + c_{2} e^{- 2 (2 + 3) t}

9 y^{^{''}} - 4 y = 0

y^{^{''}} - 6 y^{^{'}} + 90 y = 0

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 9 y = 0

y^{^{''}} + 20 y^{^{'}} + 100 y = 0

y^{^{''}} + 6 y^{^{'}} + 9 y = 0, y (- 1) = 5

What is the solution for (d^2x)/(dt^2)+8(dx)/(dt)+4x=0 ?
The solution for (d^2x)/(dt^2)+8(dx)/(dt)+4x=0 is x=c_{1}e^{2(sqrt(3)-2)t}+c_{2}e^{-2(2+sqrt(3))t}