# Solution of differential equation $x dy-y dx=0$ represents:

$(A)\;a\; rectangular\; hyperbola\quad(B)\;parabola\; whose\; vertex \;is\; at \;origin \quad(C)\;straight \;line\; passing\; through \;origin \quad(D)\;a \;circle\; whose\; centre\; is\; at\; origin$

Toolbox:
• If an equation has n arbitary constants. then its differential equation will be of $n^{th}$ order
• Equation of a straight line pasing through the orgin is $y=mx$
Let us consider the equation of a stright line $y=mx$, which passes through the orgin.
Now differentiation with respect to x we get,
$y=mx$
$\large\frac{dy}{dx}$$=m Substituting this for m in y=mx we get y=\large\frac{dy}{dx}$$.x$
$=>y.dx=x.dy$
or $xdy-ydx=0$
Hence the correct option is $C$