Linear Differential Equations with Constant Coeffi cients 3-29
12.
−
1
1
x
D
.
Ans:
+1x
13.
−
2
2
1
1
x
e
D
.
Ans:
2
1
3
x
e
14.
−
2
2
1
4
x
e
D
.
Ans:
2
1
4
x
xe
15.
4
2
1
x
D
.
Ans:
6
1
30
x
16.
−
2
1
()
ax
e
Da
.
Ans:
2
1
2
ax
xe
3.2 GENERAL SOLUTION OF LINEAR
EQUATION
=()()fDyQx
We have seen that if
p
yy=
is a particular solution (containing no arbi-
trary constants) of the linear equation
()()fDyQx=
and
c
yy= is the
general solution of the homogenous equation ()0fDy= with as many
arbitrary constants as the order of the equation then
cp
yyy=+ is the
general solution (G.S.) of the non-homogenous linear equation:
()()fDyQx=
As we have studied methods of fi nding y
c
and the general method ...
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