When we write y = f(x) or y = g(t).  x or t is called the independent variable (meaning we can choose its value freely), and y is called the dependent variable (meaning its value is determined by the x or t value we choose).

			If a function has only one independent variable (usually x or t), then any equation involving the independent variable (say t) and the dependent variable (y) and its derivatives (y', y'',...) is called an ordinary differential equation (ODE).  That is:  y'(t) = f(y,t) or y''(t) = g(y,y',t).

			If a function has more than one independent variable (usually y = f(x,t) or z = g(x,y,t)), then any equation involving the independent variables and the dependent variable and its derivatives with respect to any of its independent variables is called a partial differential equation (PDE).

			The order of an ODE is given by the degree of its highest derivative.

			A first-order ODE has a first derivative of its dependent variable and may involve its dependent variable, the independent variable and some constants:

			A second-order ODE has a second derivative of its dependent variable and may involve its first derivative, its dependent variable, the independent variable and some constants:

			A third-order ODE has a third derivative of its dependent variable and may involve …?

			First-order:  y' = g(t,y)

			Second-order:  y'' = h(t,y,y')

			n-th order:  y(n) = p(t,y,y',y'',...,y(n-1))

			Given that y = -1/(t-C) is a solution to y' = y2, find the particular solution satisfying y(0) = 1.

			y' = y2 has solution y = -1/(t-C).  Interval of existence?

			y' = x + y has solution y = -1 - x + Cex.  Interval of existence?

			s' = r1/2 has solution s = (2/3) r3/2 + C.  Interval of existence?