Dear all, I have got an problem that I have been confused about for more than three days.

Here is the problem:

Suppose that f(x,y) is a continous function on a plane domain R, and for each point $\displaystyle (x_0,y_0)\in R$, there is a unique integral curve to the following ode

$\displaystyle \frac{dy}{dx}=f(x,y).$

Show then the solution to the above ode depends continuously on the initial data.