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Differential Equations by Pearson
book

Differential Equations by Pearson

by E. Rukmangadachari
May 2024
Intermediate to advanced content levelIntermediate to advanced
472 pages
13h 25m
English
Pearson India
Content preview from Differential Equations by Pearson
2-40 Diff erential Equations
12.
2
0.
x
ydx xdy
xe dx
y
+=
Ans:
(1)
x
x
y
xec+− =
2.1.5 Inexact Equation—Reducible to Exact Equation
by Integrating Factors
Integrating factor (I.F.)
If the differential equation 0Mdx Ndy+= becomes exact when we
multiply it b
y a function
(,)xy
μ
then
(,)xy
μ
is called an integrating
factor of the equation.
Consider the equation
0yd
x xdy−=
Here
,11
MN
MyN x
yx
∂∂
==−⇒=≠=−
∂∂
The equation is not exact. If we multiply it by
2
1
y
we get
2
1
0.
x
dx dy
yy
−=
Now
2
1
,
x
y
y
MN==−
so that
2
1
.
MN
yyx
∂∂
=− =
∂∂
So, the equation becomes exact.
2
1
y
is an integrating factor. We can eas-
ily check that
222
11 1
,,
xy
xxy+
are also integrating factors for the equation.
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Publisher Resources

ISBN: 9781299487406Publisher Website