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KEAM 2015 Math Paper
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© examsnet.com
Question : 21
Total: 120
The slope of a curve at any point (x,y) other than the origin, is
y
+
y
x
.
Then the equation of the curve is
y
=
C
x
e
x
y
=
x
(
e
x
+
C
)
x
y
=
C
e
x
y
+
x
e
x
=
C
(
y
−
x
)
e
x
=
C
Validate
Solution:
Slope of a curve at
(
x
,
y
)
is given by
d
y
d
x
According to the question,
d
y
d
x
=
y
+
y
x
⇒
d
y
d
x
=
y
(
1
+
1
x
)
⇒
∫
d
y
y
=
∫
(
1
+
1
x
)
d
x
⇒
log
y
=
x
+
log
x
+
log
C
⇒
log
y
=
log
(
C
x
e
x
)
[
∵
x
=
log
e
x
]
⇒
y
=
C
x
e
x
© examsnet.com
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