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

Options

A. Rectangular hyperbola
B. Straight line passing through (0,0)
C. Parabola with vertex at (0,0)
D. Circle with centre at (0,0)

Answer

B

Explanation

Given that x dy - ydx =0
Dividing both the sides by ` x^(2)`
`Rightarrow (xdy -ydx)/(x^(2)) =0`
` Rightarrow d( y/x) =0`
` Rightarrow y/x =c Rightarrow y =cx`, where c is a constant
Thus it a straight line passing through (0,0)
Aliter :
Given , xdy -ydx =0
` Rightarrow (dy)/y = (dx)/x `
Integrating both the sides , ` int (dy)/y = int (dx)/x + log c `
`log y = log x + log c` where c is constant
`Rightarrow y = cx`