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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
Linear Diff erential Equations with Constant Coeffi cients 3-53
The general solution is
54
32
12 3
7
() 7 7.
20 4 2
x
xx
yx c cx ce x x x
⎛⎞
=++−+++++
⎜⎟
⎝⎠
Example 3.2.26 Solve
22
(2 ) .DDyx+=
Solution To fi nd the complementary function, we hav
e to solve
2
(2 ) 0DDy+=
The auxiliary equation is
+=
+= =− =+
2
2
12
20
1
(2 1) 0 0,
2
x
c
mm
mm m y c ce
To fi
nd the particular integral,
()
212 232
3
22 2 22 2
11 1
(1 2 ) 1 2 4 8
(1 2 )
1
()2 4()8 () 2 8 16
3
p
yxDxDDDx
DD D D
x
xxDxDx xx
D
==+=−+−+
+
=−+ =−+−
The general solution is
3
22
12
( ) 2 8 16.
3
x
x
yx c ce x x
=+ + +
EXERCISE 3.7
Solve the following:
1.
3
2214.yyyy x−−−=−
′′′ ′′
[JNTU 2004(3)]
Ans:
235
(5 ) 2cx x y+=
2.
()
23
1.DD yx++ =
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Publisher Resources

ISBN: 9781299487406Publisher Website