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KEAM 2018 Math Paper
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© examsnet.com
Question : 100
Total: 120
The differential equation of the family of curves
y
=
e
x
(
A
c
o
s
x
+
B
s
i
n
x
)
.
where A and B are arbitrary constants is
y
′
′
−
2
y
′
+
2
y
=
0
y
′
′
+
2
y
′
+
2
y
=
0
y
′
′
+
y
′
+
y
=
0
y
′
′
+
2
y
′
−
y
=
0
y
′
′
−
2
y
′
−
2
y
=
0
Validate
Solution:
Given, system of equation is
y
=
e
x
(
A
cos
x
+
B
sin
x
)
⇒
d
y
d
x
=
e
x
(
−
A
cos
x
+
B
cos
x
)
+
y
....(i)
⇒
d
2
y
d
x
2
=
e
x
(
−
A
sin
x
+
B
cos
x
)
+
e
x
[
−
A
cos
x
−
B
sin
x
]
+
d
y
d
x
⇒
d
2
y
d
x
2
=
(
d
y
d
x
−
y
)
y
+
d
y
d
x
[by Eq. (i)]
⇒
d
2
y
d
x
2
−
2
d
y
d
x
+
2
y
=
0
⇒
y
′
−
2
y
′
+
2
y
=
0
This is required differential equation.
© examsnet.com
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