Unformatted text preview: Therefore, we can choose s = 0, and so y p ( t ) = A cos 3 t + B sin 3 t, y p ( t ) = − 3 A sin 3 t + 3 B cos 3 t, y p ( t ) = − 9 A cos 3 t − 9 B sin 3 t. Substituting these expressions into the original equation and equating the corresponding coeﬃcients, we conclude that ( − 9 A cos 3 t − 9 B sin 3 t ) − ( − 3 A sin 3 t + 3 B cos 3 t ) + 9 ( A cos 3 t + B sin 3 t ) = 3 sin 3 t ⇒ − 3 B cos 3 t + 3 A sin 3 t = 3 sin 3 t ⇒ A = 1 , B = 0 . Hence, the answer is y p ( t ) = cos 3 t . 190...
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This note was uploaded on 03/29/2010 for the course MATH 54257 taught by Professor Hald,oh during the Spring '10 term at Berkeley.
 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations

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