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!

Homework Help: Integral curves

  1. Jan 30, 2012 #1

    fluidistic

    User Avatar
    Gold Member

    1. The problem statement, all variables and given/known data
    Find the solution to [itex]y'=\frac{y+x}{y-x}[/itex] and graph the integral curves.


    2. Relevant equations
    Exact differential equation.


    3. The attempt at a solution
    I noticed it's an exact differential equation, I solved it implicitely. I reached that [itex]\frac{y^2 (x)}{2}-\frac{x^2}{2}-yx=\text{constant}[/itex]. I've looked into wikipedia about the integral curves but I don't really know how to find them here. If I understood well, an integral curve is a solution to the DE, so here it would be any y(x) that satisfies the DE. But here I can't get y(x) explicitely, so how do I graph y(x)?... Any idea is welcome!
     
  2. jcsd
  3. Jan 30, 2012 #2

    HallsofIvy

    User Avatar
    Science Advisor

    Choose a number of specific values for the constant and graph those curves.
     
  4. Jan 30, 2012 #3

    fluidistic

    User Avatar
    Gold Member

    Ah I see, thank you very much. I graph point per point, maybe I'm missing an obvious curve or something.
    I take C=1. I set x=0 and I get [itex]y=\pm \sqrt 2[/itex]. I graph this in the x-y plane. Now I set x=2 and I get a quadratic equation for y, which yields [itex]y= 2 \pm \sqrt {10}[/itex]. So for a fixed C, there are 2 curves; maybe parabolas or hyperbolas.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook




Loading...