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1. In each of the following verify that the indicated function y = ¢(x) is an implicit solution of the given first-order differential equation. Consider ø as just a function and give its domain. Then, consider ø as a solution of the differential equation and give at least one interval I of definition a.) (y – x)y' = y – x + 8; y = x + 4/x+2 b.) y' = 25 + y²; y = 5 tan 5x

1. In each of the following verify that the indicated function y = ¢(x) is an implicit solution of the given first-order differential equation. Consider ø as just a function and give its domain. Then, consider ø as a solution of the differential equation and give at least one interval I of definition a.) (y – x)y' = y – x + 8; y = x + 4/x+2 b.) y' = 25 + y²; y = 5 tan 5x

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. In each of the following verify that the indicated function y = ¢(x) is an implicit solution of the given first-order differential equation. Consider ø as just a function and give its domain. Then, consider ø as a solution of the differential equation and give at least one interval I of definition a.) (y – x)y' = y – x + 8; y = x + 4Vx+ 2 b.) y' = 25 + y²; y = 5 tan 5 c.) 2y' = y³ cos x; y = (1 – sin x)-1/2
Transcribed Image Text:1. In each of the following verify that the indicated function y = ¢(x) is an implicit solution of the given first-order differential equation. Consider ø as just a function and give its domain. Then, consider ø as a solution of the differential equation and give at least one interval I of definition a.) (y – x)y' = y – x + 8; y = x + 4Vx+ 2 b.) y' = 25 + y²; y = 5 tan 5 c.) 2y' = y³ cos x; y = (1 – sin x)-1/2
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