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Unformatted text preview: ing to (6.19). Thus s is the smallest number m such that x m cos βx and x m sin βx are not solutions to the corresponding homogeneous equation. 39. Writing the system in operator form yields ( D 2 − 1) [ x ] + y = 0 , x + ( D 2 − 1) [ y ] = e 3 t . Subtracting the Frst equation from the second equation multiplied by ( D 2 − 1), we get n ( D 2 − 1 ) [ x ] + ( D 2 − 1 ) 2 [ y ] o − ±( D 2 − 1 ) [ x ] + y ² = ( D 2 − 1 )³ e 3 t ´ − 0 = 8 e 3 t ⇒ n ( D 2 − 1 ) 2 − 1 o [ y ] = 8 e 3 t ⇒ D 2 ( D 2 − 2 ) [ y ] = 8 e 3 t . (6.22) 374...
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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 University of California, Berkeley.
 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations

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