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Thread: 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 $\displaystyle y(0.2) \approx 1$

    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 $\displaystyle y(0.2),$ you've gone just one step.

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