Some of the second order ODE can be considered as Euler-Lagrange equations for an appropriate Lagrangian. However this is true not for arbitrary second order equation. But some of important equations of physics do satisfy this property which is called the least action principle.

I am interested in the following ODE in $\mathbb{R}^3$: $$\overset{\cdot\cdot}{\vec x}=-\overset{\cdot}{\vec x}.$$

Is it an Euler-Lagrange equation for an appropriate Lagrangian $L(\vec x,\overset{\cdot}{\vec x},t)$? If yes, what is $L$?