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Solution of the differential equation xd...

Solution of the differential equation `xdy-ydx=0` represents

A

a rectangular hyperbola

B

a straight line passing through the origin

C

parabola whose vertex is at the origin

D

circle whose centre is at the origin

Text Solution

Verified by Experts

The correct Answer is:
B
We have,
`xdy-ydx=0`
`rArr" "(1)/(y)dy-(1)/(x)dx=0`
`rArr" "logy-logx=logC" [On integrating]"`
`rArr" "(y)/(x)=C rArr y=Cx`
Clearly, it represents a straight line passing through the origin.
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