Differential Equations: An Introduction to Modern Methods and Applications

3rd Edition

ISBN: 9781118531778

Author: James R. Brannan, William E. Boyce

Publisher: WILEY

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In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied unde…

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Textbook Question

Chapter 4.2, Problem 18P

If the Wronskian W of f and g is 3 e 2 t , and if f ( t ) = e 4 t , find g ( t )

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Chapter 4.2, Problem 17P

Chapter 4.2, Problem 19P

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Example: For what odd primes p is 11 a quadratic residue modulo p? Solution: This is really asking "when is (11 | p) =1?" First, 11 = 3 (mod 4). To use LQR, consider two cases p = 1 or 3 (mod 4): p=1 We have 1 = (11 | p) = (p | 11), so p is a quadratic residue modulo 11. By brute force: 121, 224, 3² = 9, 4² = 5, 5² = 3 (mod 11) so the quadratic residues mod 11 are 1,3,4,5,9. Using CRT for p = 1 (mod 4) & p = 1,3,4,5,9 (mod 11). p = 1 (mod 4) & p = 1 (mod 11 gives p 1 (mod 44). p = 1 (mod 4) & p = 3 (mod 11) gives p25 (mod 44). p = 1 (mod 4) & p = 4 (mod 11) gives p=37 (mod 44). p = 1 (mod 4) & p = 5 (mod 11) gives p 5 (mod 44). p = 1 (mod 4) & p=9 (mod 11) gives p 9 (mod 44). So p =1,5,9,25,37 (mod 44).

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Jamal wants to save $48,000 for a down payment on a home. How much will he need to invest in an account with 11.8% APR, compounding daily, in order to reach his goal in 10 years? Round to the nearest dollar.

Chapter 4 Solutions

Differential Equations: An Introduction to Modern Methods and Applications

Ch. 4.1 - In Problems 1 through 7, determine whether the...Ch. 4.1 - In Problems 1 through 7, determine whether the...Ch. 4.1 - In Problems 1 through 7, determine whether the...Ch. 4.1 - In Problems 1 through 7, determine whether the...Ch. 4.1 - In Problems 1 through 7, determine whether the...Ch. 4.1 - In Problems 1 through 7, determine whether the...Ch. 4.1 - In Problems 1 through 7, determine whether the...Ch. 4.1 - A mass weighing stretches a spring . What is the...Ch. 4.1 - A mass attached to a vertical spring is slowly...Ch. 4.1 - A mass weighing stretches a spring . The mass is...

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