1. Not finding help here? Sign up for a free 30min 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!

Show that this ODE: (xy^2 + y^2)dx + xdy = 0, can be an exact ODE and its solutions!

  1. Sep 1, 2011 #1
    (xy2+y2)dx + xdy = 0

    the questions are:
    a. Show that the equations above can be an exact differential equations!
    b. Determine its solutions!

    Help me please because i have working on it for 3 hours and i can't find its integration factor to change the un-exact differential equation above into an exact one. I need your help..

    :cry:
     
  2. jcsd
  3. Sep 1, 2011 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Re: Show that this ODE: (xy^2 + y^2)dx + xdy = 0, can be an exact ODE and its solutio

    That equation isn't exact. But instead of trying to find an integrating factor, why don't you just separate the variables, which is easy?
     
  4. Sep 2, 2011 #3
    Re: Show that this ODE: (xy^2 + y^2)dx + xdy = 0, can be an exact ODE and its solutio

    Thanks LCKurtz, but my lecturer ask me to solve it by finding its integration factor.. I wonder how it is.. Can you give me a clue?
     
  5. Sep 2, 2011 #4

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

  6. Sep 2, 2011 #5

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Re: Show that this ODE: (xy^2 + y^2)dx + xdy = 0, can be an exact ODE and its solutio

    I don't think so unless I was sleepy when I checked it and am still asleep. I'm guessing the problem has a typo.
     
  7. Sep 2, 2011 #6

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    Re: Show that this ODE: (xy^2 + y^2)dx + xdy = 0, can be an exact ODE and its solutio

    Hmmm, I was allso sleepy :blushing: link doesn't work...
     
  8. Sep 2, 2011 #7

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Re: Show that this ODE: (xy^2 + y^2)dx + xdy = 0, can be an exact ODE and its solutio

    The link seems to work for me. It's just that the method doesn't work for this problem.
     
  9. Sep 2, 2011 #8

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Re: Show that this ODE: (xy^2 + y^2)dx + xdy = 0, can be an exact ODE and its solutio

    For what it's worth, and probably not very relevant, here's an exact DE that has the same solution set f(x,y) = C:

    [tex]-\frac{x+1}{xy}dx + \frac{x + \ln(x) -1}{y^2}dy = 0[/tex]

    I don't see any obvious way to manipulate the original DE into this form.

    To the original poster: I hope you will report back what your lecturer gives for a solution method.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook