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Math Help - Eulers Method Multiple Choice

  1. #1
    Junior Member
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    Eulers Method Multiple Choice

    Suppose Eulerís method, with increment dx, is used to
    numerically solve the differential equation dy/dx=f(x,y)
    with the initial condition that (x0, y0) lies on the solution
    curve. Let (x1, y1), (x2, y2), and so on denote the points
    generated by Eulerís method, and let y = y(x) denote the
    exact solution to the initial value problem. Which of the
    following must be true?

    Note: more than one are possible

    I. y(3) = y(x3)
    II. y2 = y1 + f (x1, y1) dx
    III. x3 = x0 + 3 dx



    My work:

    I believe it is II and III.

    III seems correct because dx is the change in x so if you multiply it by 3 and add it to the original it should give you x3. and II just looks like the Euler's formula.

    Anyone willing to confirm or correct.
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  2. #2
    MHF Contributor

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    Yes, you are right. Both II and III are true. I is just meaningless- there is no reason to think that "x3" is actually the number "3".
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