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Homework Help: DE method problem

  1. May 13, 2006 #1
    What method would be used to solve this DE, it look like a Bernoulli but isn't. I'm lost.

    y'cosx = 1-y^2

    Thanks,

    Gab
     
  2. jcsd
  3. May 13, 2006 #2
    It looks like you can separate the variables.
     
  4. May 13, 2006 #3
    Treat y' as the limiting ratio dy/dx.
    Your aim is to get the xs (and dx) on one side, and the ys (and dy) on the other side and integrate...
     
  5. May 14, 2006 #4
  6. May 14, 2006 #5
    Hint:

    [tex] \frac{dy}{dx} \,\, \frac{\cos x}{1-y^2}=1[/tex]
     
  7. May 14, 2006 #6
    Well from that I can say that y=sin(x) is a solution.

    Then I get:

    z' +(-2*tan(x))*z = 1/cos(x)

    So then I solve this linear equation:

    (sin(x) + C)/(cos(x))^2
     
    Last edited: May 14, 2006
  8. May 15, 2006 #7

    J77

    User Avatar

    The next step should be to substitute: [tex]y=\sin(u)[/tex] into the equation FrogPad gave.
     
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