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Question about multiple functions for a first order ODE

  1. Feb 3, 2016 #1
    The question is as follows:

    Suppose you find an implicit solution y(t) to a first order ODE by finding a function H(y, t) such that H(y(t), t) = 0 for all t in the domain. Suppose your friend tries to solve the same ODE and comes up with a different function F(y, t) such that F(y(t), t) = 0 for all t in the domain. Could you both be right, or must one of you be wrong?

    I'm pretty lost on this one, honestly. I thought about using the uniqueness theorem (about f(y,t)) being cts and the partial of f(y,t) w.r.t. y), but then I wasn't sure how I could relate this. Can anyone help me out?
  2. jcsd
  3. Feb 4, 2016 #2


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    ##y' = 1## is a first order ODE. ## H = y - (t + 4) = 0 ## and ## F = y - (t + 10) = 0 ## both satisfy the ODE, but are different functions. That what you mean ?
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