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Solution of the differential equation xdy – ydx = 0 represents a (A) parabola (B) circle (C) hyperbola (D) straight line

Solution of the differential equation xdy – ydx = 0 represents a
(A) parabola (B) circle (C) hyperbola (D) straight line

Grade:

2 Answers

vaibhav patil
18 Points
one year ago
the solution of the equation is D straight line
dy/y=dx/x 
has the equation 
lny=lnx+c which is
lny=lnx+lnC
so 
y=Cx 
staight line
 
Vikas TU
14149 Points
one year ago
We have,
xdy−ydx=0
⇒ 1/ydy−1/xdx=0
⇒ logy−logx=logC [On integrating]
⇒ y/x=C⇒y=Cx
Clearly, it represents a straight line passing through the origin.

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