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Byju's Answer
Standard XII
Mathematics
Formation of a Differential Equation from a General Solution
Form the diff...
Question
Form the differential equation corresponding to the function
y
=
A
e
x
+
B
e
2
x
, where
A
and
B
are arbitrary constants.
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Solution
y
=
A
e
x
+
B
e
2
x
As the roots are
x
and
2
x
.
The differential equation will be-
(
D
−
x
)
(
D
−
2
x
)
=
0
D
2
−
2
D
x
−
D
x
+
2
x
2
=
0
D
2
−
3
D
x
+
2
x
2
=
0
y
′′
−
3
x
y
′
+
2
x
2
=
0
[
∵
D
n
=
y
′′
.
.
.
.
n
]
Hence the differential equation corresponding to the function
y
=
A
e
x
+
B
e
2
x
is
y
′′
−
3
x
y
′
+
2
x
2
=
0
.
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