Solve the Euler-Lagrange equation

Using calculus of variations (optics subsection) we can show that the following Euler-Lagrange equation must be true:

with the boundary conditions and .

is a matrix of slowness values (inverse of velocity), so for every point in space we know the velocity values. Say for example this is the peaks function:

x = -2:0.05:2;
y = x';
[X,Y] = meshgrid(x,y);
s = peaks(X,Y);
imagesc(s)
xlabel('x')
ylabel('y')

represents the curve we're trying to find, which starts at the point and ends at the point (the boundary conditions).

Find by solving the Euler-Lagrange equation.