Results 1 to 2 of 2

Thread: Phase Portrait using Isoclines?

  1. #1
    Apr 2009

    Phase Portrait using Isoclines?

    I want to sketch the phase portrait (solution curves) of this DE

    $\displaystyle y'=y-x^2$

    Could I use isoclines? i.e. something like this

    $\displaystyle 0=y-x^2$
    $\displaystyle =>y=x^2$

    So i would sketch a parabola with slope 0 hairs on it? Then do the same thing for slope 1.

    $\displaystyle 1=y-x^2$
    $\displaystyle =>y=\frac{1}{x^2}$

    So i would sketch 1/x^2 with slope 1 hairs on the curve?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Aug 2008
    You can just plot small vectors at a rectangular grid of numbers in the x-y plane say from -5 to 5, the slope of the vectors of course is the value $\displaystyle y-x^2$ at each point so for example at the point (1,1), I'd draw a small line with a slope of 0. At the point (0,2), the line would have a slope of 2 and so forth. Once you understand the meaning of that, then try StreamPlot in Mathematica which plots the vector field of {x'(t), y'(t)} so if I let x=t then I'd need to plot the field {1,y-t^2} like so:

    StreamPlot[{1, y - t^2}, {t, -5, 5}, {y, -5, 5}] and that gives me the phase portrait below which I've also drawn a solution (in red) to the DE for y(0)=1.

    Also check out "Differential Equations" by Blanchard, Devaney, and Hall. It's the best reference for these types of problems.
    Attached Thumbnails Attached Thumbnails Phase Portrait using Isoclines?-phase-portrait.jpg  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Phase Space/ State Space/ Phase Portrait
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: Oct 12th 2010, 01:40 PM
  2. Phase Flow
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: Mar 11th 2010, 10:56 AM
  3. isoclines,,,never been very good with limits
    Posted in the Calculus Forum
    Replies: 4
    Last Post: Jun 7th 2008, 06:53 PM
  4. Out of phase
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: Nov 30th 2007, 02:59 PM
  5. phase portrait for ODE
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Feb 7th 2007, 07:04 AM

Search tags for this page

Click on a term to search for related topics.

Search Tags

/mathhelpforum @mathhelpforum