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UPSC NDA Math Model Paper 2
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© examsnet.com
Question : 109
Total: 120
Find the solution of the differential equation
d
x
d
y
=
e
x
y
+
x
y
e
−
x
y
=
−
l
n
c
y
e
−
x
y
=
l
n
c
y
e
−
y
x
=
−
l
n
c
y
e
−
y
x
=
l
n
c
y
Validate
Solution:
d
x
d
y
=
e
x
y
+
x
y
Put
x
=
v
y
,
then
d
x
d
y
=
v
+
y
d
v
d
y
v
+
y
d
v
d
y
=
e
v
+
v
d
v
e
v
=
d
y
y
By integrating both sides we get
∫
e
−
v
d
v
=
∫
d
y
y
−
e
−
v
=
ln
y
+
ln
c
Put v = x / y in the above equation we get
e
−
x
y
=
−
l
n
c
y
© examsnet.com
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