For a Lagrangian L(t,x,y,x',y'), they are given by:
∂L/∂x - d/dt(∂L/∂x') = 0,
∂L/∂y - d/dt(∂L/∂y') = 0.
Now, let's compute these derivatives for our Lagrangian L(t,x,y,x',y') = x² + y² - 32xy.
∂L/∂x = 2x - 32y,
∂L/∂x' = 0,
∂L/∂y = 2y - 32x,
∂L/∂y' =
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