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Standard XI
Maths
Question
If
y
=
a
e
2
x
+
b
e
−
x
, then show that
d
2
y
d
x
2
−
d
y
d
x
−
2
y
=
0
.
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Solution
Verified by Toppr
y
=
a
e
2
x
+
b
e
−
x
d
y
d
x
=
2
a
e
2
x
−
b
e
−
x
d
2
y
d
x
2
=
4
a
e
2
x
+
b
e
−
x
Putting these values in LHS, we get,
d
2
y
d
x
2
−
d
y
d
x
−
2
y
=
(
4
a
e
2
x
+
b
e
−
x
)
−
(
2
a
e
2
x
−
b
e
−
x
)
−
2
a
e
2
x
−
2
b
e
−
x
=
0
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18
Similar Questions
Q1
If
y
=
a
e
2
x
+
b
e
−
x
, then show that
d
2
y
d
x
2
−
d
y
d
x
−
2
y
=
0
.
View Solution
Q2
Show that
y
=
a
e
2
x
+
b
e
−
x
is a solution of the differential equation
d
2
y
d
x
2
−
d
y
d
x
−
2
y
=
0
.
View Solution
Q3
If y = ae
2x
+ be
−x
, show that,
d
2
y
d
x
2
-
d
y
d
x
-
2
y
=
0
.
View Solution
Q4
If
y
=
x
2
e
x
, show that
d
2
y
d
x
2
−
d
y
d
x
−
2
(
x
+
1
)
e
x
=
0
View Solution
Q5
If
y
=
e
−
x
cos
2
x
then which of the following differential equations is satisfied?
View Solution