Week 4 Material to be covered: 3.5 Homework to be handed Sept. 28 Problems: Sec 3.4: 23, 24 Sec 3.5: 2, 3, 9, 10 Prepare, but do not hand in, Playbook entries for: a) Reduction of order, b) Super-position in non-homogeneous equations, c) Undetermined coeﬃcients. This week, we will start the study of non-homogeneous linear second order diﬀerential equations. The main result are Theorem 3.5.1 (a superposition principle) and its consequence Theorem 3.5.2 (a formula for the general solution) of the equations. These results show that the general solution of the non-homogeneous equation is obtained by adding to the homogeneous equation a particular solution. Last, week, of course, we became experts in ﬁnding solutions of the homogeneous equation. So, this week (and the next) we will concentrate on ﬁnding particular solutions of non-homogeneous equations. This week, we will study the method of undetermined coeﬃcients, which applies to constant coeﬃcient equations with a special forcing term. The book presents several
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This note was uploaded on 02/01/2011 for the course MATH 427K taught by Professor Delallave during the Spring '11 term at University of Texas.