An explicit solution of a differential equation is: a) a simpler equation

b) a real number
c) a function on some domain
d) an approximation
e) a linear relation

The correct answer is c) a function on some domain.

When we talk about solving a differential equation, we are looking for a function that satisfies the equation. This function is called the solution to the differential equation.

An explicit solution means that we are able to determine the function explicitly, in terms of the independent variable and possibly some known constants. It provides a direct formula for the function that satisfies the differential equation.

To find an explicit solution, we typically use various techniques such as separation of variables, integrating factors, or solving linear differential equations. These techniques involve manipulating the differential equation algebraically to isolate the dependent variable and solve for it explicitly.

It's worth mentioning that not all differential equations have explicit solutions. In some cases, it may be impossible to express the solution in terms of elementary functions. In these situations, we might have to resort to numerical methods or approximation techniques to find an approximate solution, which is not considered an explicit solution.