4. (a) Prove that M(x, y) + N(x, y) = 0 can be made exact using an integrating factor that = f(x+y) for some N--My М--N depends only on the sum x + y if and only if the expression function f. (b) Use the integrating factor found in part (a) to solve 3+ y + xY+ (3 +x + xy) = 0.
4. (a) Prove that M(x, y) + N(x, y) = 0 can be made exact using an integrating factor that = f(x+y) for some N--My М--N depends only on the sum x + y if and only if the expression function f. (b) Use the integrating factor found in part (a) to solve 3+ y + xY+ (3 +x + xy) = 0.
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
I get how to solve it as an exact equation, but I'm not seeing how to get to the supplied expression
![**Problem 4:**
(a) Prove that \( M(x, y) + N(x, y) \frac{dy}{dx} = 0 \) can be made exact using an integrating factor that depends only on the sum \( x + y \) if and only if the expression
\[
\frac{N_x - M_y}{M - N} = f(x + y)
\]
for some function \( f \).
(b) Use the integrating factor found in part (a) to solve \( 3 + y + xy + (3 + x + xy) \frac{dy}{dx} = 0 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe7e0ba88-0786-454c-b4b5-22240a9787f4%2Fb1123b42-b98b-4694-90ee-65b8e6d940fa%2Fg07nurg_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 4:**
(a) Prove that \( M(x, y) + N(x, y) \frac{dy}{dx} = 0 \) can be made exact using an integrating factor that depends only on the sum \( x + y \) if and only if the expression
\[
\frac{N_x - M_y}{M - N} = f(x + y)
\]
for some function \( f \).
(b) Use the integrating factor found in part (a) to solve \( 3 + y + xy + (3 + x + xy) \frac{dy}{dx} = 0 \).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
