Proof that differential equation $f''(t)+2\lambda f'(t)+\omega ^2 f(t)=0$ when $\lambda\neq0$ is not an Euler-Lagrange equation.
The damped harmonic oscillator equation with a dissipative force resembles this result, and I want to know how to express it in terms of the generic Lagrangian. I've also heard about phase flow explanations and wonder how to articulate them.
If we use $q=e^{\lambda t}f$, the equation for $q(t)$ becomes an Euler-Lagrange equation. I am curious if there are essential reasons for this.
