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 \cdot \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 \cdot \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}

y^{^{'''}} - y^{^{''}} - 34 y^{^{'}} - 56 y = 0

y^{^{''}} + a y = 0, y (0) = 0, y^{^{'}} (1) = 0

9 y^{^{''}} + 36 y^{^{'}} + 100 y = 0, y (0) = 4, y^{^{'}} (0) = 9

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

\frac{d ^{2} y}{d t ^{2}} - 6 \frac{d y}{d t} - 7 y = 0

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}