1. (a) Differentiate and substitute to show that y = x - x-1 is a solution to the differential equation xy' + y = 2x. (b) Show that y = -½ x cos x is a solution to the differential equation y" + y = sin x.
1. (a) Differentiate and substitute to show that y = x - x-1 is a solution to the differential equation xy' + y = 2x. (b) Show that y = -½ x cos x is a solution to the differential equation y" + y = sin x.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 14CR
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![1. (a) Differentiate and substitute to show that y = x - x-1 is a solution to the differential
equation
xy' + y = 2x.
(b) Show that y = -½ x cos x is a solution to the differential equation
y" + y = sin x.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F321870cf-5f02-4a7a-9bd1-b1bcd10d94da%2F19369859-a0a3-48a1-87fb-51b29296e41f%2Fzq6xdt3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. (a) Differentiate and substitute to show that y = x - x-1 is a solution to the differential
equation
xy' + y = 2x.
(b) Show that y = -½ x cos x is a solution to the differential equation
y" + y = sin x.
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