2_1-2 - Solutions 2.1-2-Pages 107, 119 Problem 20 Determine...

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Solutions 2.1-2-Pages 107, 119 Problem 20 Determine whether the pairs of functions are linearly independent or linearly dependent on the real line. 22 ( ) , ( ) cos sin f xg x x π == + x Recall that =1. Therefore x x 2 2 sin cos + ) ( ) ( x g x f = . The pair is linearly dependent.
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Problem 21 Determine whether the pairs of functions are linearly independent or linearly dependent on the real line. x x x g x x f 2 3 ) ( , ) ( = = 0 , 0 , 2 3 2 3 < = > + = x x x x and x x x x Therefore the pair is linearly independent.
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Problem 33 Apply Theorems 5 and 6 to find general solutions of the differential equation. Primes denote derivatives with respect to x. 0 2 ' 3 = + y y y The characteristic equation is . The solution of the quadratic equation is 0 2 3 2 = + r r 39 4 ( 1 ) ( 2 2 31 2 2, 1 r r r ±− = ± = = ) The general solution is: x x e c e c y 2 2 1 + =
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Problem 39 Apply Theorems 5 and 6 to find general solutions of the differential equation. Primes denote derivatives with respect to x.
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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_1-2 - Solutions 2.1-2-Pages 107, 119 Problem 20 Determine...

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