- Thread starter
- #1

#### find_the_fun

##### Active member

- Feb 1, 2012

- 166

\(\displaystyle x \frac{dy}{dx} = y\)

What does an xy-plane have to do with anything? I looked up the definition of unique solutions and here it is

Let R be a rectangular region in the xy-planed defined by a <=x<=b, c<=y<=d that contains the point \(\displaystyle (x_0, y_0)\) in its interior. If f(x,y) and \(\displaystyle \frac{\partial{d} f}{\partial{d} y}\) are continuous on R then there exists some interval \(\displaystyle I_0: (x_0-h, x_0+h), h>0\) contained in [a/b] and a unique function y(x) defined on \(\displaystyle I_0\) that is a solution of the initial value problem.

That's a bit difficult to digest. How do I proceed?