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    Using Euler's method

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    Y'= 1/2 - (X)+2x when y(0)=1
    Find the exact solution of ___ O/ <<note!!!! I don't know how to put in a zero with a line going across to make a pheee.
    1a. Let h=.1 use euler & improved to approximate to get
    "Phee" of .1, phee of.2, and phee of .3

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    Please see attachment for response

    You problem is not clear, I need to guess, I think your problem is as follows, if not, please clarify.

    Problem:

    y'= 1/2 - y+2x when y(0)=1
    Find the exact solution of y(x)
    Let h=.1 use euler & improved to appoximate to get
    "Phee" of .1, phee of.2, and phee of .3

    Solution:

    We write equation of the form y'=-y+1/2+2x and

    First we solve y'= - y

    We know dy/(-y)=dx, integrate both sides to get

    -ln|-y|=x+C.

    Thus

    -y=+e^(-x-C)=+e^(-C)e^(-x) or
    -y=-e^(-x-C)=-e^(-C)e^(-x)

    Thus

    y=ke^(-x) for some constant k

    Now we solve

    y'= 1/2 - y+2x, we expect solutions to be of the form

    y=f(x)(e^(-x)), for ...

    Solution Summary

    This shows ho to use Euler's method to find an exact solution for a differential equation

    $2.19

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