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Binary relation question

  1. Sep 21, 2010 #1
    1. The problem statement, all variables and given/known data

    The binary relation [tex]\mathbb{R} \times (0, \infty)[/tex] which is identitical to

    (as I understand it) [tex]\mathbb{R} \times \mathbb{R}_{+}[/tex]

    this is supposedly the set on which the solution of the differential equation

    y' = f(t,y) is defined upon. Where y' = y/t + y^2 (no initial condition given).

    I find the solution to be

    y(t) = (2t)/(t^2 + c)

    Then I am suppose to find all maximale solution on the interval above.

    the solution is defined as follows on -infinity to infinity for an initial condition

    y(t_0) = x_0 where t_0 > 0.

    Because as I see it in Maple the solution phase portrait doesn't pass through zero if x_0 > 0.

    Then I draw the phase portrait with the above condition the it look asymptotic?

    But if I make x_0 then it I get what looks to be the real line.

    So please bare with me.

    With these two differential initial conditions I get different looking phase portrait. Does this mean that I have two maximal solutions? for this eqn?

    Last edited: Sep 21, 2010
  2. jcsd
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