Q.A person's assets start reducing so that the rate of reduction of assets is proportional to the square root of the assets existing at that moment. If the assets at the beginning are ₹10 lakhs and dwindle to ₹10,000 after 2 years, show that the person will be bankrupt in $2\dfrac29$ years from the start.

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 …