UPSC NDA Math Model Paper 9

Given: xdy - ydx = 0
xdy = ydx

dy

y

=

dx

x

Integrating both sides, we get
∫

dy

y

=∫

dx

x

lny = lnx + lnc
Since ln x + ln y = ln (xy) will be:
⇒ ln(y) = lncx
⇒ y = cx
Solution of the differential equation represents straight line passing through origin.