MATH 263 Lecture 5: Lecture 5
14 Feb 2019
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Document Summary
In today"s lecture we apply our discussion of integrating factors to derive a general solution for linear. We then state a general existence and uniqueness theorem for linear first order. In this section we will solve first order linear homogenous and linear inhomogenous equations. We should think of these problems as applications of the method of integrating factors introduced in the last lecture in the context of exact equations. First order linear equations are remarkable in that we can solve explicitly for the solution and we have a complete theory of solvability. Rst order equations can be solved by an integration factor. For linear rst order equations we can solve explicitly for the integration factor. Recall last week when we discussed autonomous equations, we looked at equations of the form, y (x) = ay + b where a and b are constants. We could use separation of variables to solve these equations.
