Final answer:
A differential equation relates the values of a function to its derivatives, and to find one, you differentiate the provided general solution and construct the equation. This is often done in the context of physical systems, such as electrical circuits or motion under resistance.
Step-by-step explanation:
The student is asking for help in finding a differential equation whose general solution is provided or described. To find a differential equation, one has to identify the function that represents the general solution and then differentiate it appropriately to obtain an equation that relates the function to its derivatives. The general solution would then satisfy this differential equation. It may be necessary to take the first and second derivatives with respect to an independent variable, such as time, and substitute these derivatives back into the original equation to verify that it holds.
Moreover, when talking about physical systems like a capacitor charging or a skydiver falling with air resistance, one would write a differential equation that models the physical behavior of the system. These differential equations often contain terms that represent rates of change over time and can be integrated to find equations that give the quantity of interest as a function of time or another variable, like the charge on a capacitor.