I've been trying this all day, hopefully I'm just being stupid. The full problem is to show that two simultaneous differential equations in x(t) and y(t) have a solution that is a circle, which I believe is the circle where mu is given and a is a constant depending on initial conditions. I've reduced the problem to showing
I can't show this, so if anyone could help with that I'd be really grateful.
I'm also confused as to where I'm going wrong here:
If and then the constant in the last expression above is zero (I hope that's not my mistake!). But then we can rearrange this (when x'(t) is non-zero and x isn't mu) to get which is false in most cases. Why can't I divide through?