If I have a lagrangian, then I can get the equations of the motion using the Euler-Lagrange equations. My question is about the converse of this statement: If one knows the equations of motion, like $=0$ and $2″+32=0$, then how to derive the lagrangian (or equivalent lagrangians)? By $(x,y)$, I mean, generalized coordinates $q:=(x,y)$.
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