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# The differential equation of all circles with centre at the origin is

$\begin{array}{1 1}(1)x dy+y dx=0&(2)x dy-y dx=0\\(3)x dx+y dy=0&(4)x dx-y dy=0\end{array}$

The equation of the family of circles with center at the origin is $x^2+y^2=a^2$
$2x+2y . \large\frac{dy}{dx} $$=0 x+ y . \large\frac{dy}{dx}$$=0$
$x.dx +y.dy =0$
Hence 3 is the correct answer.