Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook