I my mathematical journey I've stumbled upon an a way to represent any circle of a radius $R$ given that the original equation is of the form: $$y=\pm \sqrt{R^2 - x^2},$$ in terms of a differential equation, we get: $$y\frac{dy}{dx} + x = 0$$
Now i was thinking on deriving a form made by myself, and was wondering how to best tackle the problem...I was thinking along the lines of an exact differential equation of the first order using the properties of the total differential. Considering that a circle can be thought of the level cuve of a cylindrical surface that can be expressed as: $$f(x,y) = C$$
Am I on the right path though? Please, no one show how to explicitly do it...a few tips should suffice.
Thank you!
Well you can start with $$x^2 + y^2 = R^2$$ and differentiate implicitly, to get $$2x+2yy'=0$$
Solve for $y'$ to get your differential equation.