Solving Linear Differential Equations with an Integrating Factor (Differential Equations 16)

Examples of solving Linear First Order Differential Equations with an Integrating Factor.

Remember that when we have to divide by X, we should be stating a condition we are placing on the differential equation. TYPICALLY, this is x greater than 0. I will take this for granted in this video. It SHOULD be stated when rewriting a differential equation. So, even though I take it for granted (and probably should have written that), YOU SHOULD DEFINITELY be writing that condition on your paper.

[mariambobat]

The teacher who made mathematics a thing of beauty for the ones who were close to giving up!

[ProfessorLeonard]

Remember that when we have to divide by X, we should be stating a condition we are placing on the differential equation. TYPICALLY, this is x>0. I will take this for granted in this video. It SHOULD be stated when rewriting a differential equation. So, even though I take it for granted (and probably should have written that), YOU SHOULD DEFINITELY be writing that condition on your paper. This condition, x>0, ALSO lets us do things like take the integral of 1/x and not have to worry about absolute value.

[VMGAMEPLAYS]

1:10:19 Might be the highlight of Professor Leonard. He told us, I'll leave you to it to try it at home and then just couldn't resist but to show us how to do it so he made sure we actually understood and got the right answer. He cares so much about his students, he is a what every professor should be like!

[AlphaNiner-ykkh]

Says he’s not gonna reteach the concept *does it anyway* I love professors like this

[chukwuemeka_]

Professor Leonard changed my life ever since i met his youtube channel. Maths topics that I found very abstract is now easy to my understanding because of you. When i finally become a prominent person in life, i would make sure to reward YOU in a priceless fashion. I owe you big time

[alexm]

The fact that you decided to solve that last problem when you didn’t have to says a lot about your character. Thanks a lot for your help!

[Sonofapoop]

I knew he couldn't resist solving the last problem 😂 you're the best professor Leonard!

[isobar]

This man is exceptional. There are those who know what they ' teach ' and then there those who can 'teach' what they 'know' ...and there is a world of difference between the two. Professor Leonard is the perfect example of the latter. He is heaven sent...may he live long and prosper.

[davidjhyatt]

I can't understand my notes, I watch video, notes now clear. Thanks!

[huligangaeddhaerika-nonan]

when I want to look for certain math tutorials in youtube, I search your channel first to see if you have a video about it. I wish all teachers are as passionate as you

[lindseytreweek]

I don't always understand it all at first, but seeing the gaps fill in as I keep practicing is so rewarding! Thank you Professor Leonard!

[Aymen]

For the example starting at 54:17, I paused the video and immediately did it by separable equations technique. Just happy that I caught that and still got the right answer!

[lastonehabombe]

You've unlocked all struggles I had professor, you're really great

[cheez]

You must get this a lot, but you are the best person to teach this on youtube, all other videos don't go over everything as concisely as you do. Merci

[emirhaninanc]

I am really appreciated for your videos. You are not only a teacher, but also a chance for us who doesn't have an instructor like you. Thanks a lot!!!

[ricocollado]

42:12 Professor be spitting bars 😮🔥
"sine of pi is 0
e to the 0 is 1
1 minus 2 is negative 1
C equals negative 1"

[josetakapele]

Resources like this make me feel like it’s going to be okay and I can pass the class.

[didriksoderstrom]

Professor, this is legit the third class in a row you are saving my grade in. Thank you.

[dougfarrell]

Prof Leonard, first off I want to express my appreciation for you taking both the time and effort out of your, I’m sure busy schedule, to create and post these great videos. It is obvious that you enjoy teaching and want to make sure your students do absolutely understand what you are teaching. I spend quite a bit of time on Youtube taking courses and I find your teaching methods very detailed, organized and easy to follow. I had many math classes while working on a physics and math degree about 50 years ago and realize that I have forgotten how to handle many problems. I enjoy going back and reviewing subjects that I did not get to cover previously or something that interest me that I want to understand better. I decided a few months ago to go back and take some more math & engineering courses. While following some MIT lectures on electromagnetism the lecturer wrote a 2nd order differential equation to solve on the blackboard. I quickly realized that I did not remember anything about how to find the solution to this type of problem. Consequently I decided to review how to solve these types of problems so that I will be able to better understand the math and science of the physics course that I was taking which led me to this course of yours. I also plan to retake your calculus courses to get myself back up on this subject again.

So that I am understanding this concept of integration factor, one question I have is on the example problem: DY/DX + 3Y = 2X e^ -3x, when you integrate [e^3x] on the left side, wouldn’t that be equal to [e^3x/3] rather than just e^3x? In this method I thought we were finding the integral of P(Q) which I thought was [e^3x] and not the quantity [3e^3X]. What am I doing wrong in this problem?

[tanmaypatel]

It's like watching Bob Ross paint. The only difference being it's Mr. Leonard instead of Mr. Ross, and he's solving differential equations instead of painting.


Every teacher and professor should have this kind of interest and enthusiasm when teaching.