# 2_2 - Solutions 2.2-Page 119 Problem 9 Use the Wronskian to...

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Solutions 2.2-Page 119 Problem 9 Use the Wronskian to prove that the given functions are linearly independent on the indicated interval. ; sin ) ( , cos ) ( , ) ( x x h x x g e x f x = = = the real line The Wronskian will be 3 x 3 because n-1 derivatives must be taken. See pg.113. The derivatives are as follows: x x h x x g e x f x x h x x g e x f x x sin ) ( cos ) ( ) ( cos ) ( sin ) ( ) ( = = = = = = 0 2 sin cos cos sin sin cos ) sin , cos , ( = = x x x x x e x x e x x e x x e x x e W

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Problem 11 Use the Wronskian to prove that the given functions are linearly independent on the indicated interval. ; ) ( , ) ( , ) ( 2 x x e x x h xe x g x x f = = = the real line The necessary derivatives are as follows: x x x x x x x x x e x xe e x h xe e x g x f e x xe x h xe e x g x f 2 2 4 2 ) ( 2 ) ( 0 ) ( 2 ) ( ) ( 1 ) ( + + = + = = + = + = = 0 4 2 2 0 2 1 ) , , ( 2 3 2 2 2 2 = + + + + + = x x x x x x x x x x x x x x e x e x xe e xe e e x xe xe e e x xe x e x xe x W if 0 x
Problem 21 A nonhomogeneous differential equation, a complementary solution , and a particular solution are given.

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## This note was uploaded on 06/06/2011 for the course EGM 3311 taught by Professor Haftka during the Spring '11 term at University of Florida.

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2_2 - Solutions 2.2-Page 119 Problem 9 Use the Wronskian to...

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