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(a) Prove that if a first order differential equation is separable then it is exact (b) First determine the given equation is exact or not and hen solve it directly or by finding the appropriate integrating factor (x² + y² − 5)dx = (y + xy) dy, y(0) = 1

(a) Prove that if a first order differential equation is separable then it is exact (b) First determine the given equation is exact or not and hen solve it directly or by finding the appropriate integrating factor (x² + y² − 5)dx = (y + xy) dy, y(0) = 1

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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I need help with this problem described below and an explanation for the solution. (Differential Equations)

(a) Prove that if a first order differential equation is separable then it is exact (b) First determine the given equation is exact or not and hen solve it directly or by finding the appropriate integrating factor (x² + y² − 5)dx = (y + xy) dy, y(0) = 1
Transcribed Image Text:(a) Prove that if a first order differential equation is separable then it is exact (b) First determine the given equation is exact or not and hen solve it directly or by finding the appropriate integrating factor (x² + y² − 5)dx = (y + xy) dy, y(0) = 1
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