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Math Help - Differential equation: Euler's method problem

  1. #1
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    Differential equation: Euler's method problem

    Hi everyone. I'm having trouble with this problem:

    Use Euler's method with step size 0.2 to estimate y(1), where y(x) is the solution of the initial-value problem y' = xy - x2, y(0) = 1.

    I did this, but I don't know if it's right. I don't even know if I understand the question. Here's what I have:

    y' = xy - x2 = x(y-x)
    = 1 + .2(0(1-0)) = 1
    So, y(1) = 1.

    Am I anywhere close? Thanks for your help.
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  2. #2
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    Re: Differential equation: Euler's method problem

    Looks OK but I'd say y(0.2) \approx 1

    If you want to understand better this MIT Math Lecture: Differential Equations - 02 - Euler's Method for y'=f(x,y) might help.
    Thanks from kethgr
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  3. #3
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    Re: Differential equation: Euler's method problem

    What you have calculated (so far) is the Euler approximation to y(0.2), you've gone just one step.

    You now have to move on successively to approximations for y(0.4), y(0.6), y(0.8), and finally y(1).
    Thanks from kethgr
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