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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 2-61
Put
1
2
1
tan ,
1
y t dy dt
y
==
+
()
1
1
2
2
2tan
tan
1
2
1
.
2
t
t
y
y
cedt
ce
xe c e
=+
=+
=+
Example 2.1.69 Solve
2
cos tan .
dy
xy x
dx
+=
[JNTU 1999S]
Solution Writing the equation as
22
sec tan sec
dy
xy x x
dx
+=
Here
22
() sec , () tan sec .Px x Qx x x==
This is linear in y. Also,
2
tan
() sec tan
Integrating factor
x
Pxdx xdx x
e
==
=
∫∫
The general solution is
tan 2 tan
tan sec
xx
ye c x xe dx=+
Put
2
tan , secxt xdxdt==
(1)
t
t
ctedt
ct e
=+
=+
Integrating by parts
tan
(tan 1).
x
yce x
=+−
Example 2.1.70 Solve
40.xy y++=
[JNTU 2001]
Solution Writing the equation in the form
14
,
dy
y
dx x x
+=−
Ch02.indd 61Ch02.indd 61 12/9/2011 ...
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Publisher Resources

ISBN: 9781299487406Publisher Website