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Homework Help: Solving a problem regarding Existence theorem.

  1. Sep 15, 2015 #1
    1. The problem statement, all variables and given/known data
    Given the equation dy/dx = y^4 - x^4, y(0) = 7, determine whether the existance/uniqueness theorem implies that the given initial value problem has a unique solution.

    2. Relevant equations
    Existence/Uniqueness Theorem

    3. The attempt at a solution
    To my understanding, you must assign f(x,y) = y^4 - x^4 then derive f(x,y) in terms of y.

    f'(x,y) = 4y^3

    This is as far as I have gotten.
  2. jcsd
  3. Sep 15, 2015 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    What is the statement of the existence/uniqueness theorem? How does it apply in your case?
  4. Sep 16, 2015 #3
    I need to use the theorem to determine of the equation dy/dx = y^4 - x^4 has a unique solution at point (0,7). Is that correct?
  5. Sep 16, 2015 #4


    Staff: Mentor

    That isn't what Ray asked. What does the Existence and Uniqueness Theorem say?
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