certain differential equation has the form f(x)dx + g(x)h(y)dy = 0. th none of the functions f(x), g(x), h(y) identically 0. Show that a necessary d sufficient condition for this equation to be exact is that g(x) : = constant.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
A certain differential equation has the form
f(x)dx + g(x)h(y)dy = 0.
with none of the functions f(x), g(x), h(y) identically 0. Show that a necessary
and sufficient condition for this equation to be exact is that g(x) = constant.
Transcribed Image Text:A certain differential equation has the form f(x)dx + g(x)h(y)dy = 0. with none of the functions f(x), g(x), h(y) identically 0. Show that a necessary and sufficient condition for this equation to be exact is that g(x) = constant.
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
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…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,