Linear Differential Equations with Constant Coeffi cients 3-47
Example 3.2.16 Evaluate
32
1
sin2.
1
x
DDD+++
Solution
()()
()
()
3222
2
2
11
sin2sin2
111
11
sin2sin2
3(1)31
(sin2)1sin2
2cos2sin2
.
32115
xx
DDDDDD
D
xx
DD
Dxx
xx
=
++++++
−
==
−+−−
−⋅
−
==
−−−
Example 3.2.17 Ev
aluate
2
2
1
sin.
4
x
D−
Solution
20.
2222
2
111cos21111
sincos2
4422424
111111
1cos2cos2.
204224816
x
x
xex
DDDD
xx
−
⎛⎞
==−⋅
⎜⎟
⎝⎠
−−−−
=⋅−⋅=−+
−−−
Example 3.2.18 Solve
2
(32)sin3.DDyx−+=
(3.70)
Solution To fi nd the complementary function, we have to solve
2
(32)0DDy−+=
(3.71)
The auxiliary equation is
2
320(1)(2)01,2mmmmm−+=⇒−−=⇒=
2
12
xx
c
ycece=+
(3.72)
To fi nd the ...
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