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Math Help - Continuous Depending On the Data

  1. #1
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    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 (x_0,y_0)\in R, there is a unique integral curve to the following ode
    \frac{dy}{dx}=f(x,y).
    Show then the solution to the above ode depends continuously on the initial data.
    Last edited by Ackbeet; July 7th 2011 at 04:14 AM.
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  2. #2
    A Plied Mathematician
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    Re: Continuous Depending On the Data

    That's in Coddington and Levinson. You might try pages 58ff.
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  3. #3
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    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.
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  4. #4
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    Re: Continuous Depending On the Data

    Quote Originally Posted by Ackbeet View Post
    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.
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