Determine whether the equation is exact. If it is, then solve it. (3x²y + 2) dx + (x³ -1) dy = 0 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.
Determine whether the equation is exact. If it is, then solve it. (3x²y + 2) dx + (x³ -1) dy = 0 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.
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
![**Determine whether the equation is exact. If it is, then solve it.**
\[
(3x^2y + 2) \, dx + (x^3 - 1) \, dy = 0
\]
---
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 \(\boxed{\phantom{C}}\), where \( C \) is an arbitrary constant. (Type an expression using \( x \) and \( y \) as the variables.)
- **B.** The equation is not exact.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1720cd77-2294-45a6-8b70-43447dc02920%2F9db009cf-5a31-49b9-ac1d-2a2e4f6f0885%2F8bmg9s_processed.png&w=3840&q=75)
Transcribed Image Text:**Determine whether the equation is exact. If it is, then solve it.**
\[
(3x^2y + 2) \, dx + (x^3 - 1) \, dy = 0
\]
---
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 \(\boxed{\phantom{C}}\), where \( C \) is an arbitrary constant. (Type an expression using \( x \) and \( y \) as the variables.)
- **B.** The equation is not exact.
Expert Solution
Step 1
The given differential equation is ,
(.) A differential equation of the form is said to be exact if ,
(.) If the differential equation is exact , then the solution is given by ,
Note: Integrate all the terms of w.r.t. taking as constant . Integrate only those terms of w.r.t. 'y' which does not contain.
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