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Differential Equations Direction Fields: Example 2: Electric Circuit

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First published at 21:36 UTC on September 28th, 2018.

#mathematics
#calculus
#science

Math Easy Solutions

MES

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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.

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhsNZFnoROicWKcXu3w

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/differential-equations-direction-fields-example-2-electric-circuit

Related Videos:

Differential Equations: Electric Circuit: Introduction: https://youtu.be/E6vij-RzQ-o
Differential Equations: Direction Fields: Example 1: https://youtu.be/mtbMQQZeMoQ
Differential Equations: Direction Fields: https://youtu.be/zWv1y8Xp1ac
Differential Equations: General Overview: https://youtu.be/jit59tIY4UI
Differential Equations: Spring Motion: Example 1: https://youtu.be/Twu30EJ93Wg
Differential Equations: Motion of a Spring: https://youtu.be/mk2TiR5dwVs
Differential Equations: Population Growth: https://youtu.be/Td8C_cTEGkA .

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