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In this video I go over an example on differential equations and show that the family of functions y = (1 + ce^t) / (1 - ce^t), where c is a constant, is a solution to the differential equation y' = 1/2(y^2 - 1). The process of proving that it is indeed a solution is to simply take the derivative of the family of functions and ensure that it satisfies the differential equation, which I show that it clearly does.
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhsFwy6vbLODQ0spUnA
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/differential-equations-example-1
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
Derivative Rules - Proof of the Quotient Rule: http://youtu.be/fJcgnLKkISE
Foil Method - Simple Proof and Quick Alternative Method: http://youtu.be/tmj_r94D6wQ .
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