Linear Differential Equations: Example 1

In this video I go over an example on solving linear differential equations from the methods of my last video. In this example I go over the solution of the differential equation: y' + 3x^2*y = 6x^2. The first step in solving this is to first recall the form of the "integrating factor" I(x), and then multiple both sides of the differential equation by it. This results in the left side being equal to the derivative of the combined function I(x)y, also resulting in a separable equation, which I have shown before the methodolgy on solving it. The solution is found to be y(x) = 2 + Ce^(-x^3), which I plot out for varying values for the constant C. This is a pretty extensive and useful example on solving linear differential equations, so make sure to watch this video!

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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 Logarithms and their Properties - An Introduction: http://youtu.be/AZ6KKym19gI .

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