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What kind of ODE is this?

  1. Jul 15, 2016 #1
    upload_2016-7-15_16-38-10.png
    consider ODE :
    upload_2016-7-15_16-38-46.png
    Show that the solution to this ODE is:
    upload_2016-7-15_16-40-23.png

    Can someone tell what kind of ODE is it?I thought,it's on the form of Bernoulli ODE with P(x)=0.Is it possible to still solve it by using Bernoulli Methodology?I mean by substituting u=y^1-a with a=2?

    Thanks
     
  2. jcsd
  3. Jul 15, 2016 #2

    Twigg

    User Avatar
    Gold Member

    It's separable. Divide both sides by ##y^{2}##, multiply both sides by dx, and you'll see what I mean.
     
  4. Jul 15, 2016 #3

    Mark44

    Staff: Mentor

    The DE is a first order, non-linear differential equation. It's first order, since the highest derivative is a first derivative. It's nonlinear, since the dependent variable is not first-degree.

    As Twigg points out, it turns out to be separable, so you can manipulate it to get y and dy on one side and x and dx on the other. Solving DEs by separation is one of the first techniques presented in most diff. equation textbooks.
     
  5. Jul 16, 2016 #4
    Thanks Guys!
     
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