Determine whether the equation is exact. If it is, then solve it. y = ¾ ]dy = 0 7 [ 1 1 1 1 cos (xy). dx + x cos (xy) - 2y Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The equation is exact and an implicit solution in the form F(x,y) = C is = C, where C is an arbitrary constant. (Type an expression using x and y as the variables.) OB. The equation is not exact.
Determine whether the equation is exact. If it is, then solve it. y = ¾ ]dy = 0 7 [ 1 1 1 1 cos (xy). dx + x cos (xy) - 2y Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The equation is exact and an implicit solution in the form F(x,y) = C is = C, where C is an arbitrary constant. (Type an expression using x and y as the variables.) OB. The equation is not exact.
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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![**Educational Content Transcription:**
**Title:** Examining the Exactness of Differential Equations
---
**Problem Statement:**
Determine whether the following differential equation is exact. If it is, then solve it:
\[
\left[ y \cos(xy) + \frac{7}{\sqrt{1-x^2}} \right] dx + \left[ x \cos(xy) - 2y - \frac{4}{7} \right] dy = 0
\]
---
**Task:**
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
- **A.** The equation is exact and an implicit solution in the form \( F(x,y) = C \) is \(\_\_\_ = C\), where \( C \) is an arbitrary constant.
*(Type an expression using \( x \) and \( y \) as the variables.)*
- **B.** The equation is not exact.
---
**Instructional Note:**
To determine if the differential equation is exact, check if the partial derivative of \( M \) with respect to \( y \) equals the partial derivative of \( N \) with respect to \( x \). If they are equal, the equation is exact, and you can find a potential function \( F(x, y) \) to solve the equation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1720cd77-2294-45a6-8b70-43447dc02920%2Fe5167d2c-2df3-4119-bd9e-b58ee1176a6f%2Ftui69zr_processed.png&w=3840&q=75)
Transcribed Image Text:**Educational Content Transcription:**
**Title:** Examining the Exactness of Differential Equations
---
**Problem Statement:**
Determine whether the following differential equation is exact. If it is, then solve it:
\[
\left[ y \cos(xy) + \frac{7}{\sqrt{1-x^2}} \right] dx + \left[ x \cos(xy) - 2y - \frac{4}{7} \right] dy = 0
\]
---
**Task:**
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
- **A.** The equation is exact and an implicit solution in the form \( F(x,y) = C \) is \(\_\_\_ = C\), where \( C \) is an arbitrary constant.
*(Type an expression using \( x \) and \( y \) as the variables.)*
- **B.** The equation is not exact.
---
**Instructional Note:**
To determine if the differential equation is exact, check if the partial derivative of \( M \) with respect to \( y \) equals the partial derivative of \( N \) with respect to \( x \). If they are equal, the equation is exact, and you can find a potential function \( F(x, y) \) to solve the equation.
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