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th Math 340 Lecture – Introduction to Ordinary Differential Equations – April 18 , 2016 What We Covered: 1. Course Content – Chapter 9: Linear Systems with Constant Coefficients a. Section 9.9: Inhomogeneous Linear Systems i. Definition: You’re given the linear equation = + () where f(t) is the inhomogeneous term because it’s not dependent on y ii. Theorem: Suppose that y is p particular solution to the inhomogeneous equation and that 1 2..., frm a fundamental set of solutions to the associated ′ homogeneous equation = . Then the general solution to the inhomogeneous equation is given by = + + +...+ , where C , 1 1 2 2 1 C2, and C nre arbitrary constants 1. This basically means you have the equation = + s youneed to set up y like you usually would, where you find the eigenvectors and create n the general equation. Then you’re goal in section 9.9 is to find y p iii. Fundamental Matrices