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Unformatted text preview:  t 3  = t 3 = y 1 ( t ). (c) Yes, because there is no constant c such that y 2 ( t ) = cy 1 ( t ) is satisFed for all t (for positive t we have c = 1, and c = 1 for negative t ). (d) While y 1 ( t ) = 3 t 2 on ( , ), for the derivative of y 2 ( t ) we consider three dierent cases: t < 0, t = 0, and t > 0. or t < 0, y 2 ( t ) = t 3 , y 2 ( t ) = 3 t 2 , and so W [ y 1 , y 2 ]( t ) = t 3 t 3 3 t 2 3 t 2 = t 3 ( 3 t 2 ) 3 t 2 ( t 3 ) = 0 . Similarly, for t > 0, y 2 ( t ) = t 3 , y 2 ( t ) = 3 t 2 , and W [ y 1 , y 2 ]( t ) = t 3 t 3 3 t 2 3 t 2 = t 3 3 t 2 3 t 2 t 3 = 0 . 173...
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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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