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

This preview shows pages 1–5. Sign up to view the full content.

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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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.
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 + =

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Problem 39 Apply Theorems 5 and 6 to find general solutions of the differential equation. Primes denote derivatives with respect to x.
This is the end of the preview. Sign up to access the rest of the document.

## 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.

### Page1 / 5

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

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online