Originally Posted by

**karatekid** Hi guys,

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 $\displaystyle {(x-\mu)}^2 + y^2 = a$ where mu is given and a is a constant depending on initial conditions. I've reduced the problem to showing $\displaystyle x\dot{y} - y\dot{x} - \mu \dot{y} = const.$

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 $\displaystyle x = a\cos{\omega t} + \mu$ and $\displaystyle y = a\sin{\omega t}$ 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 $\displaystyle \dot{y}/\dot{x} = y/(x-\mu)$ which is false in most cases. Why can't I divide through?

Thanks!!