MATH 263 Lecture 4: Lecture 4
14 Feb 2019
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Document Summary
In today"s lecture we continued our discussion of separation of variables (end of lecture 3) and introduced exact di erential equations as well as the concept of an integrating factor. Today we continue our discussion of rst order di erential equations which can be solved by exact methods, i. e. , direct integration. So far, using the method of separation of variables, we have been able to solve rst order ordinary di erential equations of the form, y (t) = f (t) y (t) = g(t)h(y) The next class of equations we will solve by direct integration are called exact di erential equations. In this lecture we will study di erential equations of the form, In this lecture we consider the x variable to be the independent variable and the y variable to be the dependent variable. Hence we assume that in some interval y can be written as a function of x.
