# Thread: Continuous Depending On the Data

1. ## Continuous Depending On the Data

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.

2. ## Re: Continuous Depending On the Data

That's in Coddington and Levinson. You might try pages 58ff.

3. ## Re: Continuous Depending On the Data

Thank you very much. I am a Chinese, and could not have access to that book. Shall you give some hints (and some steps) on it? Best wishes.

4. ## Re: Continuous Depending On the Data

Originally Posted by Ackbeet
That's in Coddington and Levinson. You might try pages 58ff.
A classic. I still have mine!

Levinson was my instructor for my first course in Linear Algebra. Never had a class under Coddington.