O.D.E plots with Matlab
Dr. John Polking (Rice U.) has developed two powerful Matlab m-files for visualization of
integral curves of first-order ODE, and trajectories of first-order systems of ODE. The most recent
versions are (respectively): dfield7.m and pplane7.m. They can be downloaded freely from the site:
(Just copy the desired m-file with your browser, then open the script m-file editor on
your Matlab and paste it to a blank page. You may wish to save both m-files to a specific
Matlab directory- I call mine odetools, for instance.)
After the m-file is saved, it can be used with no further knowledge of Matlab! The reason
is that each file includes a user-friendly graphical interface (display). For dfield7.m, you simply
enter the desired equation (in "standard form"). Hitting "proceed" gives you the direction field
(=field of line segments tangent to integral curves), and then clicking on a point in the plane
generates the integral curve through that point.
Rk: Please send me an e-mail if you decide to this- let me know if it is working, and feel free to ask questions.
And if you really get into this, there is a book to guide you in exploring these two m-files in detail
(learning a lot about Matlab and differential equations in the process). It is:
Ordinary Differential Equations using Matlab, by John C. Polking and David Arnold, Prentice-Hall (3rd ed., 2004)