For each of the following equations, find the most general function N(x,y) so that the equation is exact. (a) [9y sin (5xy) + e*]dx + N(x,y)dy = 0 (b) [ye 8xy - 4x y + 1]dx + N(x,y)dy = 0 (a) Select the correct choice below and fill in the answer box to complete your choice. (Type an expression using x and y as the variables.) O A. +h(x), where h(x) is an arbitrary function of x. B. 9x sin 5xy + g(y), where g(y) is an arbitrary function of y. (b) Select the correct choice below and fill in the answer box to complete your choice. (Type an expression using x and y as the variables.) O A. +h(x), where h(x) is an arbitrary function of x. B. + g(y), where g(y) is an arbitrary function of y.
For each of the following equations, find the most general function N(x,y) so that the equation is exact. (a) [9y sin (5xy) + e*]dx + N(x,y)dy = 0 (b) [ye 8xy - 4x y + 1]dx + N(x,y)dy = 0 (a) Select the correct choice below and fill in the answer box to complete your choice. (Type an expression using x and y as the variables.) O A. +h(x), where h(x) is an arbitrary function of x. B. 9x sin 5xy + g(y), where g(y) is an arbitrary function of y. (b) Select the correct choice below and fill in the answer box to complete your choice. (Type an expression using x and y as the variables.) O A. +h(x), where h(x) is an arbitrary function of x. B. + g(y), where g(y) is an arbitrary function of y.
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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![For each of the following equations, find the most general function \( N(x, y) \) so that the equation is exact.
(a) \( \left[ 9y \sin(5xy) + e^x \right] dx + N(x, y) dy = 0 \)
(b) \( \left[ y e^{8xy} - 4x^6 y + 1 \right] dx + N(x, y) dy = 0 \)
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(a) Select the correct choice below and fill in the answer box to complete your choice.
(Type an expression using \( x \) and \( y \) as the variables.)
- A. \(\ \square + h(x), \) where \( h(x) \) is an arbitrary function of \( x \).
- B. \(\ \checked 9x \sin 5xy + g(y), \) where \( g(y) \) is an arbitrary function of \( y \).
(b) Select the correct choice below and fill in the answer box to complete your choice.
(Type an expression using \( x \) and \( y \) as the variables.)
- A. \(\ \checked + h(x), \) where \( h(x) \) is an arbitrary function of \( x \).
- B. \(\ \square + g(y), \) where \( g(y) \) is an arbitrary function of \( y \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1720cd77-2294-45a6-8b70-43447dc02920%2Fc5f362a4-7bd6-43c2-b855-dee45cac27dc%2Ff0euntr_processed.png&w=3840&q=75)
Transcribed Image Text:For each of the following equations, find the most general function \( N(x, y) \) so that the equation is exact.
(a) \( \left[ 9y \sin(5xy) + e^x \right] dx + N(x, y) dy = 0 \)
(b) \( \left[ y e^{8xy} - 4x^6 y + 1 \right] dx + N(x, y) dy = 0 \)
---
(a) Select the correct choice below and fill in the answer box to complete your choice.
(Type an expression using \( x \) and \( y \) as the variables.)
- A. \(\ \square + h(x), \) where \( h(x) \) is an arbitrary function of \( x \).
- B. \(\ \checked 9x \sin 5xy + g(y), \) where \( g(y) \) is an arbitrary function of \( y \).
(b) Select the correct choice below and fill in the answer box to complete your choice.
(Type an expression using \( x \) and \( y \) as the variables.)
- A. \(\ \checked + h(x), \) where \( h(x) \) is an arbitrary function of \( x \).
- B. \(\ \square + g(y), \) where \( g(y) \) is an arbitrary function of \( y \).
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