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UPSC NDA Math Model Paper 5
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© examsnet.com
Question : 52
Total: 120
What is the solution of the differential equation
d
y
d
x
+
y
x
=
0
?
where
c
is a constant
xy = c
x = cy
y = cx
None of the above
Validate
Solution:
To Find: Solution of the differential equation
d
y
d
x
+
y
x
=
0
⇒
d
y
d
x
=
−
y
x
⇒
d
y
y
=
−
d
x
x
Integrating both sides, we get
∫
d
y
y
=
−
∫
d
x
x
⇒
ln
y
=
−
ln
x
+
ln
c
⇒
ln
y
+
ln
x
=
ln
c
⇒ ln(xy) = lnc (∵ ln x + ln y = ln (xy))
∴ xy = c
© examsnet.com
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