Which one of the following differential equation has the solution xy = c ? a) ydy + xdx = 0 b) xdy + ydx = 0 c) xdy ydx = 0 d) ydy xdx = 0

To determine which differential equation has the solution $xy=c$, we differentiate both sides with respect to $x$:

$$\frac{d}{dx}(xy)=\frac{d}{dx}(c)$$

Using the product rule on the left side:

$$y+x\frac{dy}{dx}=0$$

Rearranging terms:

$$x\frac{dy}{dx}+y=0$$

Multiply both sides by $dx$ to express in differential form:

$$xdy+ydx=0$$

This matches option (b).

Thus, the correct answer is (b).