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Linear Differential Equations: Integrating Factor
In this video I go over the integrating factor, which is used in solving linear differential equations, in great detail to illustrate that we only ever need just one particular solution of it. When deriving the solution of a linear differential equation, see my earlier video, I first had to derive the integrating factor I(x). In that derivation, as well as in my earlier examples, I showed since we only need to have just one particular I(x), we can simply choose any values for the constants of integrations that arise, preferrable those that make I(x) as simple as possible (without making I(x) equal to zero). But in those videos, I did not mathematically prove why we only need just one particular solution. So, in this video I show how even if we didn't choose any values for the constants, that at the very end, those constants simply get combined into the final constant integration of the solution. Thus, it does not matter what value those constants are, and we can simply choose any values we want (again assuming we don't get a non-zero value of I(x)). This is a very interesting video on the integrating factor, which isn't explained to this level of detail in most math classes, so make sure to watch this video!
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhtt8s1sXtWUEJ9O49w
Related Videos:
Linear Differential Equations: Example 2: https://youtu.be/cHEmdWBFt0I
Linear Differential Equations: Example 1: https://youtu.be/YW_QJ7RQlBY
Linear Differential Equations: https://youtu.be/T3MliJDBaxc
Differential Equations: Exponential Growth and Decay: https://youtu.be/DZtDUIZuxcg
Differential Equations: Separable Equations: https://youtu.be/pBV-xT9ty94
Power Functions and their Properties Part 1 - A Simple Explanation: http://youtu.be/2MKko4ZkSf0 .
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