A differential equation is any equation which contains derivatives, either ordinary derivatives or partial derivatives. As shown by the equations given below, a derivative may be invoolved implicitly through the presence of differentials. The following are examples of differential equations:

Families of curves are the set of curves whose equations are of the same form but have different values assigned to one or more parameters

During the first week of discussion, I have learned that differential equations is analogous to college algebra for it also solve systems of equations containing derivatives for an unknown function y = f(x). It always contains the derivatives of one or more functions with respect to two or more independent variables. Thus, differential equation can be classified according to type, order, and linearity.

The study of differential equations is also the same as in integral calculus, as its solution can be graphed into families of curves. A solution containing arbitrary constants is called a one-parameter family of solutions. Meanwhile, an nth-order differential equations always seek for an n-parameter family of solutions, which means that a single differential equation can possess an infinite number of solutions. Inversely we can obtain the differential equation through the use of elimination of arbitrary constants. It can be solved through substitution method, elimination, or using determinant.