Introduction to First-Order Differential Equations

where we understand that y is a function of an independent variable t . (We use t because in many examples the independent variable happens to be time, but of course any other variable could be used. In current versions of Maple, the dependence of y on t must be explicit, i.e., one must write y(t).) It is sometimes convenient to use informal notation and refer to this example as y′ = 0 (a physicist would write ẏ = 0), but such notation blurs the distinction between functioons and the expressions used to define them. If y′ = 0, y must be constant. In other words, the general solution of the given equation is y ≡ c, for some constant c. Another easy example of a differential equation is: