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NDA Math Differential Equation
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© examsnet.com
Question : 47
Total: 70
If
x
d
y
=
y
d
x
+
y
2
d
y
,
y
>
0
and
y
(
1
)
=
1
then what is
y
(
−
3
)
equal to?
[NDA II 2016]
3 only
−
1
only
Both
−
1
and 3
Neither
−
1
nor 3
Validate
Solution:
Given,
x
d
y
=
y
d
x
+
y
2
d
y
⇒
1
=
4
x
d
x
d
y
+
y
2
x
⇒
d
x
d
y
+
y
=
x
y
⇒
d
x
d
y
−
x
y
=
−
y
...(1)
P
=
−
1
y
,
Q
=
−
y
IF
=
e
∫
P
d
y
=
e
∫
−
1
y
d
y
=
e
−
logy
=
1
y
Multiplying Eqn. (1) by IF
⇒
1
y
d
x
d
y
−
x
y
2
=
−
1
x
y
=
∫
1
y
(
−
y
)
d
y
+
C
⇒
x
y
=
∫
−
1
d
y
+
C
⇒
x
y
=
−
y
+
C
y
(
1
)
=
1
1
1
=
−
1
+
C
⇒
C
=
2
⇒
x
y
=
−
y
+
2
⇒
x
=
−
y
2
+
2
y
⇒
y
(
−
3
)
⇒
−
3
=
−
y
2
+
2
y
⇒
y
2
−
2
y
−
3
=
0
⇒
y
=
+
2
±
√
4
+
12
2
=
2
±
4
2
⇒
y
=
3
,
−
1
Since
y
>
0
so
y
=
3
© examsnet.com
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