Sketching simple coupled oscillators

[MathCreature]

If I'm given dx/dt = 2π - sin(y - x), dy/dx = 2π - sin(x - y), and finally the conditions x(0) = pi/2 and y(0) = 0,
what would be the best way to hand sketch the solutions without using an explicit solution?

 

[Grinkle]

Find an expression for dy/dt. This seems like a homework problem, so I won't tell you exactly how to do that, but you have the information you need to do that.

Then use your expressions for dx/dt and dy/dt to generate pairs of (x,y) for increasing t, you know what to start from, as its a given in your problem. You need to think about what dx/dt and dy/dt represent to make the table correctly.

 

[Mark44]

Thread closed. The OP has been asked to repost the question in one of the Homework & Coursework sections, using the homework template to include the efforts so far.