This is from a past paper (from a lecturer I don't particularly understand)
Homework Statement
a) {4 marks} Find the Euler-Lagrange equations governing extrema of I subject to J=\text{constant} , whereI=\int_{t_1}^{t_2}\text{d}t \frac{1}{2}(x\dot{y}-y\dot{x})=\int f(t,x,y,\dot{x},\dot{y})...