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4.2 Consider the following propositions: 1) If it is known that the differential equation Mr.ude + N(x, y)dy = 0) is exact and, furthermore, its general solution is given by F(x, y) = C, then it is true that F(x, y) = [N(x, y)dy +t(x). II) The differential equation (y sen(x) - e"x²) dx + (cos(r) - e³r³) dy = 0 is NOT exact. Which of them are true? a) Only II b) None c) Only I

4.2 Consider the following propositions: 1) If it is known that the differential equation Mr.ude + N(x, y)dy = 0) is exact and, furthermore, its general solution is given by F(x, y) = C, then it is true that F(x, y) = [N(x, y)dy +t(x). II) The differential equation (y sen(x) - e"x²) dx + (cos(r) - e³r³) dy = 0 is NOT exact. Which of them are true? a) Only II b) None c) Only I

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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4.2 Consider the following propositions: 1) If it is known that the differential equation M(r.de + N(x, y)dy = 0 is exact and, furthermore, its general solution is given by F(x, y) = C, then it is true that F(x, y) = [ N(x, y)dy + t(x). II) The differential equation (y sen(x) - e¹x²) dx + (cos(x) - e¹x³) dy = 0 is NOT exact. Which of them are true? a) Only II b) None c) Only I d) Both
Transcribed Image Text:4.2 Consider the following propositions: 1) If it is known that the differential equation M(r.de + N(x, y)dy = 0 is exact and, furthermore, its general solution is given by F(x, y) = C, then it is true that F(x, y) = [ N(x, y)dy + t(x). II) The differential equation (y sen(x) - e¹x²) dx + (cos(x) - e¹x³) dy = 0 is NOT exact. Which of them are true? a) Only II b) None c) Only I d) Both
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