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Perplexed by this simple problem Please help

  1. Sep 21, 2008 #1
    dy/dx = (y-1)^2 given the initial condition y(0) =1 find an explicit solution.

    separation of variables gives:

    (y-1)^-2 dy = dx

    integrating both sides I get

    -(y-1)^-1 = x + c

    -1= (y-1)(x+c)

    -1/(x+c) = y - 1

    y= 1 - 1/(x+c) but how can the intial condition work?

    no value of c will make 1= 1 - 1(0+c)
  2. jcsd
  3. Sep 22, 2008 #2
    Pretty sure y = 1 is a fixed point (or a collection thereof, the whole y = 1 line) so you can't have any solution involving that condition since all solutions are basically just integral curves. Therefore all solutions/integral curves will either approach the y = 1 line or go away from it depending on its stability.
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