MATH 2243 Lecture Notes - Lecture 1: System Of Linear Equations, Nonlinear System
Document Summary
Let the following be true, so it will look like a 1st order de in w. This is not separable, but it is linear. Since we are looking for any w1 that satisfies the homogeneous de. You can guess the form of the solution based on the form of g(t). Since g(t) looks like e^(-t), it will look like that. Differentiate, substitute into de, and find what a is. This is not a solution to the nonhomgoeneous equation, it solves the homogeneous equation. The coefficients of functions of t must be equal. For t, the form of g(t) is appropriate for undetermined coefficients. We can assume y=e^(rt) since the de is constant coefficient. Multiply out (important, since this will give a linear output with b"s, instead of a nonlinear output with a"s) Sub into de, collect coefficients of functions of t. This will give 5 equations for the 5 unknowns b1-b5. Note we had 6 a"s and 7 b"s.
