MTH 256 Lecture 8: 01252019
10 Feb 2019
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Ex. (3xy + 2y + 2) dx + (x2 + x)dy = 0 mmmm. O is exact checking the exactness here to check your work. It hy - sin c y )) y" = o dx t ( fg - i. It exactness doesn"t work try something else . In this lesson, we consider a certain type of di erential equation which show up in many application situations. A rst order di erential equation is said to be autonomous if it can be written as dy dt. The rate function f does not depend on the independent variable t. Here are a few useful properties of rst order autonomous di erential equa- tions: they are separable, the slopes in the direction eld only depend on y. Y= htt is a general solution then y. I: the general solution is invariant under horizontal translations. This common model assumes that the rate of growth in q is proportional to itself: dq dt.
