Math 391 Lecture 3 - The integrating factor method and homogeneous 1st order ODEs. In this lecture, we continue to discuss ways of solving various first order ODEs, which is the focus of chapter 2 of Boyce/DiPrima. We focus our attention first on first order linear ODEs, in particular, those that are not separable. We look at the method of integrating factors to solve such equations, after deriving what the needed integrating factor must be. We then move on to homogeneous differential equations--a bit of a misnomer, since we will see later that "homogeneous" usually refers to something else--but we look at ways to turn such equations into separable ones with a powerful substitution technique. We did several examples of applying the integrating factor method here, but only one example of dealing with homogeneous 1st order ODEs; we will pick up with more examples next time.
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