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Linear Differential Equations: Example 3

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First published at 07:57 UTC on March 19th, 2018.

Math Easy Solutions

MES

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In this video I go over another example on linear differential equations, and this time solve the equation: y' + 2xy = 1. The solution to this equation involves having to solve the integral of e^(x^2), which as explained in my earlier video titled "Can We Integrate All Continuous Functions?", there is no possible solution to this integral using the common functions, or elementary functions, which we are used to. That being said, I use an online calculator to solve for this integral, which involves the use of a special non-elementary function, erfi(x), which is known as the imaginary error function. I also plot this the solution using a pretty advanced online calculator, and have put the link in the notes, so that you can play around with it. This is a very interesting video on linear equations, as well as the imaginary error function, which I will cover in future videos, so stay tuned for more!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhtxKz9LwWqIt7rHXkA

Related Videos:

Linear Differential Equations: Integrating Factor: https://youtu.be/HeddiAVY_NU
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
Can We Integrate All Continuous Functions?: http://youtu.be/OFEDLJYqYps .

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