week_04_4.6 - MATH2860U Chapter 4 cont 1 HIGHER-ORDER DIFF...

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MATH2860U: Chapter 4 cont… 1 HIGHER-ORDER DIFF EQNS cont… Note: You are also responsible for 4.4 (short answer and multiple choice type questions only) Variation of Parameters (Section 4.6 of Zill and Cullen, pg. 157) Recall: We began this chapter with an interest in solving the equation ) ( ) ( ) ( ) ( ) ( ) ( 0 1 1 1 1 x g y x a dx dy x a dx y d x a dx y d x a y L n n n n n n Over the past few days, we began our study by considering solutions to homogeneous 2 nd order equations, starting with the case of constant coefficients. Let us now return to studying non homogeneous equations, but first we need to recall a few things we learned in section 4.1: the general solution y c of the related homogeneous ODE 0 ) ( c y L is called the complementary solution . Any function y p that is free of arbitrary parameters and satisfies the nonhomogeneous equation ) ( ) ( x g y L p is called a particular solution . The general solution of the nonhomogeneous equation is
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week_04_4.6 - MATH2860U Chapter 4 cont 1 HIGHER-ORDER DIFF...

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