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Differential Equations: Separable Equations

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First published at 23:20 UTC on August 30th, 2018.

#mathematics
#calculus
#science

Math Easy Solutions

MES

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In this video I go over the concept of separable equations which are a type of differential equations that are possible for us to solve explicitly. A separable equation is a first-order differential equation in which both the independent and dependent variable can be separated in such a way as to write the derivative as being equal to a function of the first variable multiplied by a function of the other variable. This allows the differential equation to be "separated" in such a way that all the variables of one type are on side of the equation and the others on the other side. This gives the opportunity to apply an integral to both sides of the equation and thus serves as implicitly showing the solution of the differential equation. Depending on the complexity of the separable equation, it may be possible to solve for the solution directly.

This method of separable equations was first used by James Bernoulli and later general derived in a paper by his brother John Bernoulli. In fact the Bernoulli family is one of the most famous families in history and have a major role in shaping the foundation of mathematics. Thus, I have also gone over a brief history on the Bernoulli family in this video, so make sure to watch it!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhslZnkXJpxBkSeAonQ

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/differential-equations-separable-equations

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