Differential Equations with Boundary-Value Problems

9th Edition

ISBN: 9781337632515

Author: Dennis G. Zill

Publisher: Cengage Learning US

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Textbook Question

Chapter 4.3, Problem 62E

To solve y⁽⁴⁾ + y = 0, we must find the roots of m⁴ + 1 = 0. This is a trivial problem using a CAS but can also be done by hand working with complex numbers. Observe that m⁴ + 1 = (m² + 1)² – 2m². How does this help? Solve the differential equation.

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Chapter 4.3, Problem 61E

Chapter 4.3, Problem 63E

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Chapter 4 Solutions

Differential Equations with Boundary-Value Problems

Ch. 4.1 - In Problems 14 the given family of functions is...Ch. 4.1 - In Problems 14 the given family of functions is...Ch. 4.1 - In Problems 14 the given family of functions is...Ch. 4.1 - In Problems 14 the given family of functions is...Ch. 4.1 - Given that y=c1+c2x2 is a two-parameter family of...Ch. 4.1 - Find two members of the family of solutions in...Ch. 4.1 - Prob. 7E Ch. 4.1 - Use the general solution of x + 2x = 0 given in...Ch. 4.1 - In Problems 9 and 10 find an interval centered...Ch. 4.1 - In Problems 9 and 10 find an interval centered...

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To solve y (4) + y = 0, we must find the roots of m 4 + 1 = 0. This is a trivial problem using a CAS but can also be done by hand working with complex numbers. Observe that m 4 + 1 = ( m 2 + 1) 2 – 2 m 2 . How does this help? Solve the differential equation.

Solution Summary: The author explains the general solution to the differential equation y(4)+y=0.

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Chapter 4 Solutions