1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

First Order ODE

  1. Jul 21, 2014 #1
    1. The problem statement, all variables and given/known data

    dy/dx = x/(x2y + y3)

    2. Relevant equations

    3. The attempt at a solution

    The middle term is what's throwing me off. I can't put it in terms of y = vx (Dividing by x2 means that the y term gets screwed up. (It would turn it into yv2). Out of curiosity, I tried flat-out substituting y = vx (and turning dy/dx into x*dv/dx + v), but that didn't work either. It's obviously not exact, and I don't see how it could be made linear, so I'm not sure where to begin.
  2. jcsd
  3. Jul 21, 2014 #2
    Doesn't look like there's an elementary solution to this: http://www.wolframalpha.com/input/?i=dy/dx=x/(x^2y+y^3)
  4. Jul 21, 2014 #3
    The answer will involve the Lambert W function. Is this something you are familiar with? Basically, one arrives at something like ##z + \ln z = c## (or ##c = ze^z##) and needs to solve for ##z##.

    Start by substituting ##u = y^2## and then do another substitution. This should give you a separable equation which, after you solve it, gives you something like ##v - \ln v = g(x)##. This would be where the Lambert W function comes into play.

    Edit: If you don't like Lambert's W function, you can find a function ##h## such that ##x = h(y)##.
    Last edited: Jul 21, 2014
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Discussions: First Order ODE
  1. First-Order ODE (Replies: 17)

  2. First order ode (Replies: 5)

  3. First order ODE. (Replies: 12)

  4. First Order ODE (Replies: 11)