Question

Form the differential equation from the following primitive where constants are arbitrary:
xy = a²

Answer 1

The equation of family of curves is \[xy = a^2\]                                                   ...(1)
where a is an arbitrary constant.
This equation contains only one arbitrary constant, so we shall get a differential equation of first order.
Differentiating equation (1) with respect to x, we get
\[y + x\frac{dy}{dx} = 0\]
It is the required differential equation.