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Math Help - Graphing and Euler's Method

  1. #1
    Junior Member Coop's Avatar
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    Question Graphing and Euler's Method

    Hi,

    Part "a" of my problem says

    "Let y = y(x) be the solution to the initial-value problem

    y' = x^2 - y/3, y=y(x), y(1)=0

    Use Euler's method with n = 3 steps to estimate the value of y(2) show your steps clearly..."

    Anyway, I found the values and they are correct, shown below,

    x_0 = 1
    y_0 = 0
    x_1 = 4/3
    y_1 = 1/3
    x_2 = 5/3
    y_2 = 8/9
    x_3 = 2
    y_3 = 139/81

    But my problem is with part b,

    Graphing and Euler's Method-2010-mt1-problem-5b.png <- from the answer key

    It' asking me to graph my values with the graph of the actual solution, which isn't given. How am I supposed to figure out what the actual solution looks like?

    Thanks
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  2. #2
    MHF Contributor
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    Re: Graphing and Euler's Method

    The problem does not ask you to draw the graph of the actual solution. It asks you to write the "primary relation" of the graph of the approximation to the graph of the solution. If what is below the picture is the answer, then it seems that the "primary relation" is that the first segment of the approximation is tangent to the graph of the solution.

    You can see the solution in WolframAlpha.
    Thanks from Coop
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  3. #3
    Junior Member Coop's Avatar
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    Re: Graphing and Euler's Method

    Oh wow that is easy then, thank you

    But what does the "primary" in "primary relation" mean?
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