# 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 Preview

See attachment please!

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

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#### 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.

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