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I will be starting the control systems track at my university in a couple of weeks, so naturally I have been brushing up on my skills concerning the solution of DEs and difference equations. I was just wondering if there is an easy way to generate some of the graphs of a 1-parameter family of solutions to a first order ODE using MATLAB? (Particularly implicit solutions.) For example, an implicit solution to the simple ODE

(cosxsinx – xy^2)dx + y(1 – x^2)dy = 0

is given by

y^2(1 – x^2) – (cosx)^2 = c.

Because the equation is exact its solution is routine, but since my freshmen year I have always thought the family of curves it generates (especially near x=0) to be fairly interesting, so one of the first things I tried to do with my new copy of MATLAB was to generate this family for a few values of c… so far without success.

Anyway, my question is:

Does MATLAB have some sort of contour plot application for producing the level curves of a two variable function of the form G(x,y) = c ?

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# MATLAB and contour plots

Can you offer guidance or do you also need help?

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