Overview
We at last see how to solve a differential equation  at least for a certain type of DE, the socalled "separable differential equations". Along the way, we will learn how to use DEs to construct some useful models for physical phenomena, solve them, and analyze their behavior.
Basic Learning Objectives
These are the tasks you should be able to perform with reasonable fluency when you arrive at our next class meeting. Important new vocabulary words are indicated in italics.

Be able to put a given DE in the standard form \(\frac{dy}{dt} = g(y) h(t)\).

Be able to solve simple separable DEs.
Advanced Learning Objectives
In addition to mastering the basic objectives, here are the tasks you should be able to perform after class, with practice:

Be able to solve a separable DE.

Construct (from scratch) a DE that is a model for a given situation and solve it if it is a separable DE.
To prepare for class

Watch the following video which explains what separable DE are:

Read the detailed solution for Example 7.4.2 and pay careful attention to how the constant \(C\) is updated in the final steps of the solution. Note as well how the equilibrium solution is also taken into account in the final solution.

Watch the following video which shows another example of a separable DE. In particular, in this example, we are given an initial condition, and we obtain a single answer and not a family of solutions.

Watch the following videos which show more examples:

If necessary, you can find more examples on the web if you search for separable differential equations.

Do the Preview Activity for this section (on WeBWorK if required by your teacher).
After class

Watch the following videos which show examples of modeling reallife situations with differential equations (some of these are also described in section 7.5 in your textbook, which is optional reading):