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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
Diff erential Equations of First Order and First Degree 2-49
Example 2.1.52 Solve
() 0.x y dx dy−−=
Solution
,1,
1, 0;
10
1()
1
MN
yx
Mxy N
MN
yx
px
N
∂∂
∂∂
=− =−
∂∂
=− =
∂∂
−−
===
(Constant can be considered as a function of x.)
By Rule 3, the
() 1
integrating factor is .
p x dx dx x
eee
∫∫
==
Multiplying by the integrating factor
,
x
e=
the equation can be
written as
()(1)
xxx xx
xe dx ye dx e dy x e ye c=+⇒−=+
or 1.
x
xy ce
=++
Example 2.1.53 Solve
22
(3 2 ) ( 2 ) 0.xy y dx x xy dy−+−=
Solution
22
32, 2
34, 22
Mxyy Nx xy
MN
xy xy
yx
MN
yx
=− =−
∂∂
=− =−
∂∂
∂∂
∂∂
(3 4 ) (2 2 )
(2)
21
( ), a function of
(2)
MN
yx
xy xy
Nxxy
xy
px x
xx y x
∂∂
∂∂
−−−
=
===
By Rule 3, the
1
( ) log
integrating factor ...
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Publisher Resources

ISBN: 9781299487406Publisher Website