The differential equation of all circles which pass through the origin and whose centre is on y-axis, is
Answer & explanation
Correct answer: option 1
The differential equation representing the given family of circle is
$\left(x^2-y^2\right) \frac{d y}{d x}=2 x y$
or, $\frac{d y}{d x}=\frac{2 x y}{x^2-y^2}$
Clearly, it is a homogeneous differential equation.