(3xy + y² )dx + (x² + xy)dy = %3D

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

Differential Equation

4. Show that the given differential equation is NOT exact, and then use an integrating
factor to solve the equation.
(3xy + y² )dx + (x² + xy)dy = 0
Transcribed Image Text:4. Show that the given differential equation is NOT exact, and then use an integrating factor to solve the equation. (3xy + y² )dx + (x² + xy)dy = 0
Expert Solution
Step 1

Note that this equation is in fact homogeneous .But let us use the technique of exact and nonexact to solve it.Let us follow these steps:

Equation given that

(3xy+y2)dx+(x2+xy) dy=0 ------(1)

Here M(x, y)=3xy+y2 and N(x, y)=x2+xy

We have (\partial M/\partial y)=3xy+2y                 (\partial N/\partial x)=2x+y

Which clearly implies that the equation is not exact.

steps

Step by step

Solved in 3 steps with 10 images

Blurred answer
Knowledge Booster
Differential Equation
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
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,