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What is the integrating factor of the given differential equation (2xy - 1) dæ + æ³ dy dy = 0 ? O z-1

What is the integrating factor of the given differential equation (2xy - 1) dæ + æ³ dy dy = 0 ? O z-1

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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Exact / Non exact Differential equation (9)
What is the integrating factor of the given differential equation (2xy - 1) dæ + æ³ dy dy = 0 ? O z-1
Transcribed Image Text:What is the integrating factor of the given differential equation (2xy - 1) dæ + æ³ dy dy = 0 ? O z-1
Expert Solution
Step 1

We have,

2x2y-1dx+x3dy=0

For a differential equation of the form Mdx+Ndy=0 to be an exact differential equation,it must satisfy ∂M∂y=∂N∂x.

Here,

M=2x2y-1N=x3

So, here we have:

∂M∂y=2x2∂N∂x=3x2

Since,

∂M∂y≠∂N∂x

So,

The given differential equation is not exact.

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