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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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