Wronskian - = 0 , 1 , x, cos 3 x, sin 3 x Question 2...

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MAT 2384-Practice Problems on independence of solutions of ODEs and the Wronskian Question 1 For each of the following higher orer ODEs, use the Wronskian to show that the given functions form a basis of solutions. 1. y (4) = 0 , 1 , x, x 2 , x 3 2. x 2 y 000 - 3 xy 00 + 3 y 0 = 0 , 1 , x 2 , x 4 3. y 000 - 3 y 00 + 3 y 0 - y = 0 , e x , xe x , x 2 e x 4. y (4) + 9 y 00
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Unformatted text preview: = 0 , 1 , x, cos 3 x, sin 3 x Question 2 Determine if the given functions are linearly independent or dependent on the positive x-axis. 1. 1 , e x , e-x 2. ln x, ln( x 2 ) , (ln x ) 2 3. sin 2 x, sin x, cos x 4. cos 2 x, sin 2 x, cos 2 x 1...
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This note was uploaded on 02/24/2010 for the course SITE MAT2384 taught by Professor Josephkhoury during the Fall '09 term at University of Ottawa.

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