Determine whether the equation is exact. If it is, then solve it. (2xy + 4)dx + (x - 4) dy = 0 For the given equation, write out the condition for exactness. dx
Determine whether the equation is exact. If it is, then solve it. (2xy + 4)dx + (x - 4) dy = 0 For the given equation, write out the condition for exactness. dx
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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![**Determine whether the equation is exact. If it is, then solve it.**
\[
(2xy + 4)dx + \left( x^2 - 4 \right) dy = 0
\]
---
**For the given equation, write out the condition for exactness.**
\[
\frac{\partial}{\partial y} \left( \text{\_\_\_} \right) = \frac{\partial}{\partial x} \left( \text{\_\_\_} \right)
\]
---
To determine if the equation is exact, check if the partial derivative of \( M(x, y) \) with respect to \( y \) is equal to the partial derivative of \( N(x, y) \) with respect to \( x \), where:
- \( M(x, y) \) is the coefficient of \( dx \)
- \( N(x, y) \) is the coefficient of \( dy \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F02c9694f-8959-437e-bd84-546c9a464c26%2F22993f44-1033-4d3a-a1a6-c78a17ade12c%2Fi4k6wz_processed.png&w=3840&q=75)
Transcribed Image Text:**Determine whether the equation is exact. If it is, then solve it.**
\[
(2xy + 4)dx + \left( x^2 - 4 \right) dy = 0
\]
---
**For the given equation, write out the condition for exactness.**
\[
\frac{\partial}{\partial y} \left( \text{\_\_\_} \right) = \frac{\partial}{\partial x} \left( \text{\_\_\_} \right)
\]
---
To determine if the equation is exact, check if the partial derivative of \( M(x, y) \) with respect to \( y \) is equal to the partial derivative of \( N(x, y) \) with respect to \( x \), where:
- \( M(x, y) \) is the coefficient of \( dx \)
- \( N(x, y) \) is the coefficient of \( dy \)
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