As opposed to normal equations where the solution is a number, a differential equation is one where the solution is actually a function, and which at least one derivative of that unknown function is part of the equation.
As with finding antiderivatives of a function, we are often left with a solution that encompasses more than one possibility (consider the many possible values of the constant “c” typically found in antiderivatives). The set of functions which answer any differential equation is called the “general solution” for that differential equation. Any one function out of that set is referred to as a “particular solution” for that differential equation. The variable of reference for differentiation and integration within the differential equation is known as the “independent variable.”
by Jeff Child
by Jake Hertz