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Homework Help: Infinite Solution to a differential equation problem

  1. May 3, 2012 #1
    Give an example of an everywhere continuous function F such that the initial value problem y' = F(y), y(0) = 0 has infinitely many solution.

    The only function that I have thought of so far that has infinite solutions is y=ey + c, but that obviously doesn't fall under the condition of y(0) = 0.
  2. jcsd
  3. May 3, 2012 #2
    Do you remember the requirement for uniqueness of solutions to differential equations?
    If you have a differential equation of the form y'(x) = f(y), where f(y) is continuous, but not Lipschitz continuous, then that might work!
  4. May 3, 2012 #3


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    "Lispschitz" lies part way between "continuous" and "has a continuous derivative" (many textbooks give "has a continuous derivative" as a sufficient but not necessary condition for existence and uniqueness) so if you use a function that is continuous but does not differentiable with respect to y, that will be sufficient.
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