as an extension to the normal brachistochrone problem:
$$T[y]=F(y,y')= \tfrac{1}{\sqrt{2g}}\int_{0}^{x_{b}}\tfrac{\sqrt{1+(y'(x))^2}}{\sqrt{y(x)}}dx$$
I was asked to get the gravity dependent on x, so the new formula would be
$$T[y]=F(y,y')= \tfrac{1}{\sqrt{2}}\int_{0}^{x_{b}}\tfrac{\sqrt{1+(y'(x))^2}}{\sqrt{y(x)g(x)}}dx$$
This new problem must be solved numerically, so I played around with the step size N and value of the increase of g, if we see g as linear. I got the following graphical plots:
My professor now asks me, how can it be, that the values for y at x=0 are seemingly negative (apart from a and b in the first pictures) in in some of the pictures and why the curves are oscilatting so strongly.