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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
2-26 Diff erential Equations
The given differential equation can be written as
Sum of numerators
2 5 1 5 2 1 Sum of denominators
Difference of numerators
Difference denominators
dy dx
xy xy
==
++ +−
=
() ()
7( ) 3( ) 2
dy x d y x
xy yx
+−
==
+−+
Integrating
11
log ( ) log (3 3 2) const.
73
xy y x+= −++
Simplifying we can write the general solution as
73
(3 3 2) ( )yx Cyx−+ = +
Example 2.1.29 Solve
653
42
dy x y
dx x y
+−
=
++
Solution Here
6, 5, 3
4, 1, 2
abc
lmn
===−
===
65
14 0
41
ab
lm
==−≠
0.bl+≠ (case (6(ii)))
Put ,xX
hyYk=+ =+ and choose ,hk so that
6530hk+−=
and 420hk++=
i.e.
11312
(,) ,
13 24 14 14 7
hk
hk
⎛⎞
==⇒ =−
⎜⎟
⎝⎠
−−
Now the differential equation transforms to
65
,
4
dY X Y
dX
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Publisher Resources

ISBN: 9781299487406Publisher Website