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Question
Mathematics
The order of the differential equation associated with the primitive y=c1+c2 ex+c3 e-2 x+c4, where c1, c2, c3, c4 are arbitrary constants, is
Q. The order of the differential equation associated with the primitive
y
=
c
1
+
c
2
e
x
+
c
3
e
−
2
x
+
c
4
, where
c
1
,
c
2
,
c
3
,
c
4
are arbitrary constants, is
291
236
Differential Equations
Report Error
A
3
B
4
C
2
D
None of these
Solution:
We have
y
=
c
1
+
c
2
e
x
+
c
3
e
−
2
x
+
c
4
⇒
y
=
c
1
+
c
2
e
x
+
c
3
e
−
2
x
⋅
e
c
4
⇒
y
=
c
1
+
c
2
e
x
+
c
3
′
e
−
2
x
,
where
c
3
′
=
c
3
e
c
4
It is an equation containing three arbitrary constants.
So, the associated differential equation is of order
3
.