Determine whether the equation is exact. If it is, then solve it. 7 ]dy = 0 y cos (xy) + 7 [x cos(x dx + x cos (xy)-2y Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 7 14 3 The equation is exact and an implicit solution in the form F(x,y) = C is sin (xy) + sin −1(x)- 1y³ = C, where C is an arbitrary Einmanin oy) A. constant. (Type an expression using x and y as the variables.) Wrong OB. The equation is not exact.
Determine whether the equation is exact. If it is, then solve it. 7 ]dy = 0 y cos (xy) + 7 [x cos(x dx + x cos (xy)-2y Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 7 14 3 The equation is exact and an implicit solution in the form F(x,y) = C is sin (xy) + sin −1(x)- 1y³ = C, where C is an arbitrary Einmanin oy) A. constant. (Type an expression using x and y as the variables.) Wrong 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
Related questions
Question
![**Mathematical Problem Explanation:**
Determine whether the equation is exact. If it is, then solve it.
Equation:
\[
\left[ y \cos(xy) + \frac{7}{\sqrt{1-x^2}} \right] dx + \left[ x \cos(xy) - 2y - \frac{4}{7} \right] dy = 0
\]
---
**Instructions:**
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:
\[
\sin(xy) + \sin^{-1}(x) - \frac{14}{3}y^{\frac{7}{3}} = C
\]
where \( C \) is an arbitrary constant. (Type an expression using \( x \) and \( y \) as the variables.)
- **B.** The equation is not exact.
**Indicator:**
A blue checkmark indicates option A is selected, accompanied by the annotation "Wrong" in blue handwriting, pointing to option A.
---
The problem requires verifying the exactness of a given differential equation and finding a solution if it is exact. The options suggest determining the appropriate method and justification for the provided equation and its solution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1720cd77-2294-45a6-8b70-43447dc02920%2F81dfa600-c2b4-417c-a794-e22451346de1%2Fm89qeox_processed.png&w=3840&q=75)
Transcribed Image Text:**Mathematical Problem Explanation:**
Determine whether the equation is exact. If it is, then solve it.
Equation:
\[
\left[ y \cos(xy) + \frac{7}{\sqrt{1-x^2}} \right] dx + \left[ x \cos(xy) - 2y - \frac{4}{7} \right] dy = 0
\]
---
**Instructions:**
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:
\[
\sin(xy) + \sin^{-1}(x) - \frac{14}{3}y^{\frac{7}{3}} = C
\]
where \( C \) is an arbitrary constant. (Type an expression using \( x \) and \( y \) as the variables.)
- **B.** The equation is not exact.
**Indicator:**
A blue checkmark indicates option A is selected, accompanied by the annotation "Wrong" in blue handwriting, pointing to option A.
---
The problem requires verifying the exactness of a given differential equation and finding a solution if it is exact. The options suggest determining the appropriate method and justification for the provided equation and its solution.
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