The vast majority of the following example will not be done in any of the remaining examples and the work that we will put into the remaining examples will not be shown in this example. The whole point behind this example is to show you just what an exact differential equation is, how we use this fact to arrive at a solution and why the process works as it does. The majority of the actual solution details will be shown in a later example. For this example the function that we need is. Do not worry at this point about where this function came from and how we found it.
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Given a function f x, y of two variables, its total differential df is defined by the equation. Therefore, if a differential equation has the form. In this case,. To determine whether a given differential equation.