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 nonhomogeneous equations, c) Undetermined coeﬃcients.
This week, we will start the study of nonhomogeneous 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 nonhomogeneous 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 nonhomogeneous 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.
 Spring '11
 DELALLAVE
 Differential Equations, Equations

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