Linear Differential Equations with Constant Coeffi cients 3-53
The general solution is
54
32
123
7
()77.
2042
x
xx
yxccxcexxx
⎛⎞
=++−+++++
⎜⎟
⎝⎠
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
(21)00,
2
x
c
mm
mmmycce
To fi
nd the particular integral,
()
212232
3
222222
111
(12)1248
(12)
1
()24()8()2816
3
p
yxDxDDDx
DDDD
x
xxDxDxxx
D
−
==+=−+−+
+
=−+−=−+−
The general solution is
3
22
12
()2816.
3
x
x
yxccexx
−
=++−+−
EXERCISE 3.7
Solve the following:
1.
3
2214.yyyyx−−−=−
′′′′′′
[JNTU 2004(3)]
Ans:
235
(5)2cxxy+=
2.
()
23
1.DDyx++=
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