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First Order Differential Equations where a<x<b (Intial value?)

  1. Feb 12, 2013 #1
    Hi, I'm having trouble understanding what to do when a First order equation has an inequality at the end of it.

    For example : sqrt(y-x^2y)*dy/dx = -xy where -1<x<1

    I've solved the differential equation with y = 1/4(2C*sqrt(1-x^2) + C^2 -x^2 +1) where C is a constant.

    What do I do with the inequality? Is it an initial value problem?
     
  2. jcsd
  3. Feb 13, 2013 #2

    tiny-tim

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    welcome to pf!

    hi kafuzz! welcome to pf! :smile:
    your solution contains √(1 - x2) …

    you'll probably find that if |x| > 1, you get a solution with √(x2 - 1), or maybe some inverse trig function :wink:
     
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