Q.The normal lines to a given curve at each point $(x,y)$ on the curve pass through $(2,0)$. The curve passes through $(2,3)$. Find the equation of the curve.

Beyond growth, decay and cooling, a differential equation can capture any situation where a rate of change is described in words and the underlying quantity is the actual object of interest — for example, water rising in a cone at a rate tied to the wetted curved-surface area, a raindrop evaporating at a rate proportional to its own surface area, a balloon's volume inflating at a constant rate, or a person's assets shrinking at a rate proportional to the square root of the current assets. Solving these problems has two distinct stages: first, translating the verbal description into a differential equation by identifying which rate (dV/dt, dh/dt, dr/dt, dA/dt, ...) is being described and what it is stated to be proportional (or equal) to, often requiring an extra geometric relation (such as similar triangles linking a cone's water radius to its height, or t …