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(3xy + y² )dx + (x² + xy)dy = %3D

(3xy + y² )dx + (x² + xy)dy = %3D

Advanced Engineering Mathematics
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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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.

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