## Euler Lagrange Equation

Euler-Lagrange Equation for $\int F(x, y, y’) dx$: $$\frac{d}{dx} \left( \frac{\partial F}{\partial y’} \right) = \frac{\partial F}{\partial y}$$ – Dependent variable missing, E-L equation becomes: $$\frac{\partial F}{\partial y’} = constant$$ – Independent variable missing, E-L equation becomes: $$F – y’\frac{\partial F}{\partial y’} = constant$$ _____________ Several dependent variables: E.g. $F = F (x, y_1 , y_2 , … , y_n …