Differential Equations Direction Fields: Example 2: Electric Circuit

In this video I go over an example on drawing direction fields for the differential equation that I covered in my last video that relates the voltage drops due to an inductor and resistor with the voltage and current supplied of an electric circuit. The direction field in this example is very interesting in that, since the differential equation does not depend on the time variable but only on the current, this makes every line segment parallel to every other line segment to the left or the right of it, assuming they are at the same currents. This type of differential equation is called autonomous and thus if we know one solution to the differential equation, we can obtain infinitely many, simply by shifting the solution left or right.

This video relies heavily on the definitions and concepts involved in electric circuits so make sure to watch last video before watching this if you haven't covered electric circuits before.

Related Videos:

------------------------------------------------------

[mes]

I don't always obtain a solution for the current through an electric circuit but when I do I usually can obtain infinitely many more solutions from that one solution because the differential equation is autonomous ;)