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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
3-56 Diff erential Equations
The general solution is
12 3 4
cos
() cos sin .
5
x
xx
cp
ex
yx y y ce ce c x c x
=+= + + +
Example 3.2.31 Solve
22
(44) cos.
x
DDye x
++ =
Solution To fi nd the complementary function, we have to solve
2
(44)0DDy++ =
The auxiliary equation is
22
2
12
44(2)0 2,2
()
x
c
mm m m
yccxe
++=+=⇒ =−−
=+
To fi nd the particular integral,
2
2
22
22
2
1
cos cos
(2) (22)
1
cos cos
x
x
p
xx
e
yex x
DD
exex
D
−−
==
+−+
==−
The general solution is
22
12
() () ( ) cos.
xx
cp
yx yx y y c cxe e x
−−
==+=+
EXERCISE 3.8
Solve the following:
1.
22
(76) (1).
x
DDye x−+ = + [JNTU 2003]
Ans:
2
6
12
(4 1)
16
x
xx
e
yce ce x
−−
=+ +
2.
2
(21) .
x
DDyxe−+=
Ans:
12
( ) ( sin 2cos )
xx
yccxeexx x=+ +
3.
32 2
(3 ...
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Publisher Resources

ISBN: 9781299487406Publisher Website