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    Use the Uniqueness Theorem for the Initial Value Problem

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    4. For the initial value problem dy/dx = 3y^(2/3), y(2) = 0,

    (a) does existence uniqueness Theorem 1 imply the existence of a unique solution? Explain.

    (b) Which of the following functions are solutions to the above differential equation? Explain.

    (b_1) y(x) = 0
    (b_2) y(x) = (x - 2)^3
    (b_3) y(x) = (x - alpha)^3, x < alpha
    0, alpha <= x <= Beta
    (x - Beta)^3, x > Beta

    where alpha < 2 < Beta.

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    Solution. (a) We write this differential equation as follows.

    Then we know that and are continuous at any region S of the following form where

    Solution Summary

    This solution shows how to use the uniqueness theorem to find the solution to an initial value problem in an attached Word document.