Question

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

• A. $xdy+ydx=0$
• B. $xdy-ydx=0$
• C. $xdx+ydy=0$
• D. $xdx-ydy=0$

Answer 1

The correct option is C $xdx+ydy=0$

The equation of the family of circles centered at origin, is
$x^2+y^2=R^2$ where $R$ is the radius of the circle.
Differentiating with respect to $x$ gives us
$2x+2y.\frac{dy}{dx}=0$
or
$x.dx+y.dy=0$.