# Use the Uniqueness Theorem for the Initial Value Problem

Not what you're looking for? Search our solutions OR ask your own Custom question.

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.

Â© BrainMass Inc. brainmass.com October 2, 2022, 5:33 am ad1c9bdddfhttps://brainmass.com/math/calculus-and-analysis/uniqueness-theorem-initial-value-problem-21297

#### 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

...

#### 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.

$2.49