Show that if the roots of the auxiliary equation of a differential equation are r = p± qi, then the differential equation itself is y" – 2py + (p² + q²)y = 0
Show that if the roots of the auxiliary equation of a differential equation are r = p± qi, then the differential equation itself is y" – 2py + (p² + q²)y = 0
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![7. Show that if the roots of the auxiliary equation of a differential equation are r = p+ qi, then
the differential equation itself is y" – 2py' + (p? + q?)y = 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcb5e3d88-b796-4443-b241-fc3b9985c73a%2F77619587-f3b7-4fc1-8b6b-3166e868fe13%2F8am797f_processed.png&w=3840&q=75)
Transcribed Image Text:7. Show that if the roots of the auxiliary equation of a differential equation are r = p+ qi, then
the differential equation itself is y" – 2py' + (p? + q?)y = 0
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