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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
4-6 Diff erential Equations
1, 0
dy dy
yx
dx dx
=+=
Integrating we get
y = x + c, y
2
+ x
2
c
2
= 0
combined solution is
(y x c) (y
2
+ x
2
c
2
) = 0
Example 4.1.11 Solve x + yp
2
= p (1 + xy).
Solution x + yp
2
= p (1 + xy)
x xpy = p yp
2
x (1 yp) = p (1 yp)
(p x) (yp 1) = 0
,1==
dy dy
xy
dx dx
Integrating we get
2
2
1
,
22
=+ =+
y
yxc xc
combined solution is
22
11
–– 0
22
yxc y–xc
⎛⎞⎛
=
⎜⎟⎜
⎝⎠⎝
Example 4.1.12 Solve xp
2
+ (y x) p y = 0.
Solution xp
2
+ (y x) p y = 0
xp
2
xp + yp y = 0
(p 1) (xp + y) = 0
1, 0=+=
dy dy
xy
dx dx
Integrating we get
y = x + c, xy + c = 0
combined solution is
(y x c) (xy + c) = 0
Ch04.indd 6Ch04.indd 6 12/9/2011 11:49:00 ...
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Publisher Resources

ISBN: 9781299487406Publisher Website