Unsure how to solve for dy/dx given dy/dt and dx/dt

I seem to have forgotten how to solve basic problems in calculus. Let's say dy/dt=x, dx/dt=y, and initial conditions are something like x(0)=xnot and y(0)=ynot. If I want to solve for dy/dx in terms of x and y, my initial thought is simply to divide but the initial conditions suggest otherwise. It seems I need a refresher here.

Further, can I show my solutions lie on perhaps a hyperbola, a vertical line, or whatever it may lie on manually without let's say MATLAB?

Thanks!

https://stackoverflow.com/questions/66484776/unsure-how-to-solve-for-dy-dx-given-dy-dt-and-dx-dt March 05, 2021 at 07:54AM