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In this episode of Engineer In Training Exam TV we will reinforce your understanding of Higher Order Homogeneous Differential Equations. We will begin by defining Higher Order Homogeneous Differential Equations and then run through a few example problems.
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Justin,
I appreciate your videos. They are keeping me motivated and on track to study this math section at least.
I have a correction on your first example and the way you are explaining the substitution of “r” for y’s in the original equation. Actually the substitution of “r” is only for the derivative functions (translated, y-double prime and y-prime) in the equation. You used a “r” substitute for 9y in the equation and that is wrong. The characteristic equation should have been “r squared minus 9” (do not add the “r” to 9). Otherwise if you factor what you have with r squared minus 9r, factoring the r, you get r(r-9) which would make the roots (0,9) which it totally different than the values of (+3,-3). So when you expain the substitution, please note it is only for the dirrivative functions (prime values) of the equation. Thank you for the info nonetheless.
What do you have in study material in regards to the other 12 subjects?
Hey Johnny,
First off, I want to apologize for overlooking this comment now for some time. I hope you are well. You are absolutely correct! Thank you for bringing this to my attention. It allows me to make the appropriate corrections and/or enhancements to the content, making it better for you and my audience as a whole. Anyways, I have added an annotation on the video that explains my poor execution in explaining the concept as well as my misstep on the first step of the solution in example 1. Thank you again, and even more, thank you for taking time out of your day to help the site become a better resource for all.
Have a great day!