First Order Linear Differential Equation & Integrating Factor (introduction & example)

[@AC-vj3iy]

Dude, this literally brought tears to my eyes. I spent the past 12 hours studying this through my professor's notes and the textbook and all other videos and you explained it in 10 mins.

[@masterdon187]

*20 mins

[@GhostyOcean]

@@masterdon187 whole video is 20 minutes, but the explanation isn't the entire video.

[@BradleyCopp]

2* speed for the pros of studying

[@lanlanyiyiyi3933]

Exactly the same experience!!!!!!!!!!!!!!!!!

[@aga080]

dude...same..what.the.fuck.

[@fawazalkhelaiwi2525]

"I know this looks sexy, but this is sec(x) times y" haha

[@user-en5vj6vr2u]

heyyy sec(x)y ;)

[@real_dddf]

@@user-en5vj6vr2u let's get cos(y) together!

[@AdityaKumar-gv4dj]

sec C 😂

[@YusufSuleiman-kk6fu]

😅😂​@@AdityaKumar-gv4dj

[@andreguimaraes9347]

I always smile around the middle of his videos when I see where its all going.

[@blackpenredpen]

NicE!

[@frankpyapao6499]

Of course

[@okechukwuciano4997]

My favorite KZbin channels for learning ODEs are Blackpenredpen, Organic Chemistry Tutor, and Khan Academy. A year ago, I could not solve ODEs. Now I am smashing it. Thanks a lot dude. You're saving me in graduate school.

[@aquienpuedaimportar3028]

These videos are really superb. I love how they start with the underlying principles so you end up seeing how things work rather than just memorising a procedure. Thanks very much, blackpedredpen!

[@blackpenredpen]

Thank you very much for such the nice comment!! : )

[@thefunpolice]

Exactly right. Spot on comment.

[@NMelakis1]

17:20 "It's so Nice"!- Yes I agree. Your spirit is very refreshing! Like a cold glass of water on a 115F day. Thank you for the videos!

[@fatsquirrel75]

Truly the best explanation of the IF I've seen. Thank you so much. It finally clicks. Woohoo.

[@blackpenredpen]

Great to hear! Thanks!!!!

[@postnubilaphoebus96]

Blackpenredpen - click for clicks

[@zasgat]

can we start a gofundme to get this guy a lapel microphone

[@ridpathos7821]

My teacher: We're going to do linear first order DEs. It's OBVIOUS to everyone that you just need to multiply by this (random term he pulls from his butt) to make this work. So just guess the term that works and do it. Blackpenredpen: This is what we're doing and here's why. (Proceeds to actually EXPLAIN why and how he does things.) I'm going to need your videos this entire quarter because my teacher sucks and just assumes what is obvious to him is obvious to everyone.

[@aga080]

i cant even begin to tell you how accurate this is. i wish i had known this a month ago.

[@itsmesuryat7570]

I'm beginning to suspect that most teachers have no clue as to why the integrating factor is the way it is.

[@vinaykumar2030]

and this is how teaching should be done

[@jrddvs24]

Welp, this is the story of my life now. I have no clue why, but every word I can feel in my soul. This guy is bizarre, he explains EVERYTHING in an understandable way, since I found this guy I did not even bother looking anywhere else

[@tomatrix7525]

They all do that. When you teach something urself and do not understand it all you have to say is it is obvious in order to avoid explaining it which u cannot do.

[@jazzm5557]

YES THANK YOU FOR THIS OMG. Thanks for actually explaining how to identify the product rule!! So many other videos completely skipped that...

[@blackpenredpen]

Jazz M you're welcome!

[@fullmetalpotato1258]

This vid is probably among the most deserving of a subscribe I've ever seen dude. You are awesome!!!

[@blackpenredpen]

Fallout Nick thank you!!

[@collegeguy1325]

it took you 20 min to explain this concept in simple terms whereas my proff took two days and even then 90 percent of the class was confused! lol. Well done, thank you

[@aymankhan7905]

One of the best ways to give an introduction to the first-order linear differential equations. Explaining why we do, what we do.

[@TheodorRiegger]

The integral of tan(x) really got me! I was so confused why he got ln(sec(x)) whilst I got -ln(cos(x)), but then I realised I can just write it as -1(ln(cos(x))) and then as ln(cos(x))^-1 with the logarithm rules, which gives ln(sec(x)). Glad I caught that, love the videos ❤

[@elvinjafarli6257]

Man, you should apply for a professor at the Department of Mathematics at the University of Toronto! My prof sucks totally, and the book also sucks. You literally explained as sexy as you could!!!! Thanks a lot, still no idea why I pay 45K for?!

[@WA-hq6ls]

yeah, i feel you bro. same shit in ubc

[@TheTck90]

Our profs suck too but atleasst I’m only paying around 200 euros a semester to study in Finland :D

[@abrahamverbo3855]

You guys are paying?

[@ceciliagai79]

same story at NYU, even higher price u wouldn't believe

[@parthasur6018]

Unfortunately people are appointed to University teaching positions on the basis of their formal academic credentials (e.g. degrees, research papers published etc.) and NOT on their teaching ability! It is about time this should be corrected. How? After the completion of every course every professor should be graded from the feedback by students of the course. These grades should be recorded and evaluated by the college. Based on these evaluations the professor's academic career should be decided.

[@BAEX2013G]

Whenever I need to review a calc or leplace question, you always are there to help me out! Seriously you're helping so many of us get through this stuff! Thanks!

[@thefunpolice]

A superb explanation of a lovely technique. It was so good that I paused the video and derived the integration factor from matching terms with the product rule and then, paused again and solved the example DE which, from inspection, was really just cos(x)^2 + sin(x)^2 = 1 disguised in the form of an ODE. To be fair, I studied calculus at uni to third year between 2005-2008, covering methods in solving ODEs and PDEs, but I'd completely forgotten in the interim just how this integrating factor was obtained and to what forms of ODE it could be applied. The way you explained it could scarcely be better and I say that having had several outstanding university lecturers. Thank you so much for twenty minutes of pure entertainment and joy. You are an internet treasure.

[@FlavorWorld]

blackpenredpen is saving my grade!

[@blackpenredpen]

Glad to help!!!!!

[@raffaellucaschumann8365]

wow thank you! im majoring in maths and our prof didnt find it necessary to explain this. your video was extremely helpful!

[@blackpenredpen]

My pleasure!

[@senya9299]

Bro, I can't talk about how many hours I have spent trying to figure this out! Just thanks bro, thanks.

[@mohsenhca]

If you need brief lectures on ordinary differential equations, check out my youtube channel and personal website at mohsenhamedi.com/Lectures/ODE/LectureODE.html

[@gaurav1319]

He literally made math look sec(x)y to me

[@IamFated]

You sir are saving lives, your method of explaining complex topics is unmatched.

[@sumeirkhinda3166]

After searching around for a lot of time, I came across this, and honestly this is the best explanation about IF on KZbin. Thank you!

[@blackpenredpen]

: )))

[@yognaughty]

Bruh as soon as I'm not a poor college student anymore, I will be donating to your patreon. Dude just saved my life like Asian Jesus over here. You took such an abstract concept and clarified it so well in a practical way. Like even if there are parts that I don't fully understand I know I can still use the method now.

[@tpstrat14]

You make me feel like I’m cheating by teaching me easier ways to get the right answer and yet I feel like I’m understanding the concepts more too. That’s a nice combination. Thank you for your help and I hope you’re making a lot of money for it!

[@Maria_farah]

finding you a video that you upload 7 years ago but still helping any student out there is please. thank you

[@lukahnapeirogon8197]

Great Explanation Bro! I am currently studying this for my Chemical Engineering degree and this video explained much better than my lecturer.

[@em22beats28]

FROM THE BOTTOM OF MY HEART, THANK YOU! OMGGG I'VE BEEN SEARCHING THE INTERNET FOR LIKE 3 HOURS TILL THIS ONE VID EXPLAINED IT ALL. THANK YOU MAN GOD BLESS YOU

[@MRZEE-nf1fq]

wish my university professor was this good. thank you so much, this helped alot.

[@asotayousafzai]

There is no doubt about the quality of explanation, but the best thing about this video is the joy on your face while you are explaining it. Best of luck & keep doing the good work.

[@ammar.a2950]

I get really stuck and frustrated doing these problems, so seeing you going through it so seamlessly, is very satisfying to watch! :D Thank you for the video! IT HELPED A TON!!

[@wontpower]

Wow! We just finished diff eq. in my high school Calc class, and they never taught us how to solve non separable equations. This is incredible! Well done

[@blackpenredpen]

Will Power thank you. Exact equations will be next!

[@Coggernautt]

Seriously, I've taken this class at two different schools, neither of my teachers explained this simple idea of integrating factor's origin. They just gave us the formula and expected us to memorize the process instead of teaching us the reasoning behind the idea. I'm pretty sure you saved my grade, something Khan academy couldn't even do. Almost nobody explains this connection/origin

[@blackpenredpen]

thanks!!!!! best of luck to you in ur diff eq class!!

[@JENNY9767]

THANK YOU! I was so confused in class and I think I finally got the hang of it. Thank you for explaining where everything was coming from!

[@dong8912]

The way you explained how mu(x) can be derived really cleared things up for me. Thanks for the awesome video!!

[@rokurosora2404]

That helps a lot. Every time I hear my teacher say "the product rule" I go "aghh this is gonna be painful" but I know the product rule is easy, but I never understand 'how' my teacher get the formulas, for this lesson I guess I know where it all comes from. Thank you so very much. And that sexy joke made my day haha.

[@aferolkay]

Thank you dude, I can't understand why teachers always go using the theorem/technique without establishing fundamentals. Fortunately we have you guys on the internet.

[@83zn]

I have spent 2 days trying to understand my prof. lecture note like a fool. Thanks so much for the video & Thanks god i found you.

[@mciniell]

I love how excited you get when showing a really beautiful proof. It's subtle but you can rly tell u love it, and this makes learning from you so enjoyable. Keep up the amazing work!

[@JSSTyger]

Good job. I took these courses 10+ years ago but I still find myself coming back and watching interesting videos like this.

[@blackpenredpen]

JSSTyger thank you.

[@aga080]

you have succeeded where my DE professor has failed. thank you a thousand times.

[@vinaykumar2030]

One of the best videos in this channel. Hands down!

[@infinitymfg5397]

This was an awesome video! I made a video for my students, this is one of those subjects that students seem to get stuck on.

[@blackpenredpen]

Thank you! I also checked out your vids and they are very well done!

[@habakukmurigi1651]

😂😂😂

[@Siddhantabora]

Bro i love you really...i was struggling for a day to understand the proof you only took 5mins to make me understand clearly..god bless your heart bro...lots of love ❤ from India

[@danielclipper931]

I've been watching your videos for years and you never disappoint

[@noahpritchard4214]

everything I was looking for. Gave theory behind concept, tangible example, not too slow and also not too fast. Perfect!

[@EmergedLocket0]

After 2 hours of videos i think this is the best one on the inernett on this topic, thanks man.

[@sammelnik586]

Thank you! Thank you! Thank you! I have a great Diffe professor, but I missed class the day we went over this, and I've been struggling to figure out why this worked since then! Your explanation was lovely and incredibly easy to follow!

[@bwfir3ball]

one of the best explanations I have seen. Up there with khan academy. Even made sure i watched all the ads all the way through. Keep up the good work!

[@teebiz8694]

well explained - the whole idea is to emphasize the formation of IF and its use in solving linear differential equations - very useful

[@Chamorizard]

OMG! I have been scrolling through so many videos trying to understand this until i found you! Thank you so much!! Love how passionate you are when teaching! Really inspiring !

[@hexman89]

I've been searching through all the videos about this topic but finally this one explains it step by step, no matter how easy a step may be. Thank you!!

[@priscilladoran9545]

This makes so much sense now!!!! I see what you mean about the final "punchline" part with the deriving/integrating (that really confused me at first). So it's like you have your d/dx and the v(x)*y, and to find the derivative, you integrate that piece so it stays as v(x)*y and integrate the right side! And then it's just simplifying to find y. Wowwwwww. This is great. Thank you!

[@lindyn4]

You had me at product rule...you don't know how that helped linking it back to product rule you're a super star thaaaaank you

[@azwadrahman4796]

Utterly amazing video! You focus on actually understanding the concept rather than memorizing the formula and your way of teaching is so engaging and easy to follow! Thank you so much!

[@shaharyar4093]

Your better than every professor I've ever had

[@agginswaggin]

How are you so humble and amazing at the same time????

[@NWSCS]

I have to tell you, I got as far as calculus I, and watching you do this it all made sense, and even jarred loose some forgotten trig as well. Nicely done!!!

[@vincentcarlen4052]

Hi! I just want to say that you're a great teacher! Im studying calculus at university and my teacher is really bad at explaining how and what he is doing when he shows examples. After the lessons i just watch your videos on the subject, and suddenly everything becomes much clearer. Thank you :)

[@leenaadil8474]

Thanks I have been struggling with this lesson and I have an exam in it tomorrow and just save my life 😭❤️❤️❤️❤️

[@siennawire4976]

I have been looking everywhere to figure out how to use the integrating factor as it relates to the product rule. Thank you for this video, it was so helpful!

[@zoom-jx3so]

You make this so much more fun and understandable than my professor... thank you

[@tomatrix7525]

The thing that makes it so good is the derivation, and intuition before derivation.

[@Royce133c]

This video is a god send, thank you

[@joluju2375]

It's so clear I don't even have to remember it by heart. Thanks.

[@sethholland1157]

I cannot explain just how much this video helped me. Thank you so much.

[@myfatherwillhearaboutthis7621]

You're my favorite math youtuber

[@paulkimivanramirez9468]

My modules and online lectures only explain the "how" of things, not the "why" of things. And it's especially hard for this kind of subject matter. Thank you for doing the latter excellently.

[@themichaelson]

Bro, you are a genius. 😯😯

[@the_martian_45]

I haven’t even started my senior year of high school yet (in which I will start calculus 1), and even I understand this. You are a great teacher!

[@Festus2022]

This is the BEST video on this subject I could find. Thank you. VERY CLEAR!!

[@AliBarisa]

For once, I got to know where to get myu(x) and why it's needed. Thank you for a good intro into integrating factor method for solving DE. I was having trouble with memorization, but I can just derive it whenever I happen to forget it

[@michaelgurnick8422]

This is by far the best explanation I have seen. Thank you.

[@Mustoccoli1]

When he said "this may look sexy but its sec(x)*y" I done near up and lost it

[@devenjain7116]

Thank u sir this helped me a lot in my exam and problem solving! You are the best teacher!!!! Keep shining

[@mohsenhca]

If you need brief lectures on ordinary differential equations, check out my youtube channel and personal website at mohsenhamedi.com/Lectures/ODE/LectureODE.html

[@masoncamera273]

Reverse chain rule made it so much more clear to me

[@lexsonsamson94]

Awesome teacher and the best teacher ever i came across on youtube.... thanks so much, i'm facing this part of linear constant in signals and system

[@jemcel0397]

Wow! For the first time hahaha! Congrats!! I've been looking for you when it comes to uploading Differential Equations!

[@stavem8864]

Thanks for the great video! You explained the concepts so much better than my professor.

[@MiHwAr2149]

17:48 😂😂😂😂👍👍👍 This is how great teachers glue the information in your mind, I liked it.

[@cesarmoreno987y]

dude phenomenal video. I thought you only did intro calc but you're really helping me out with differential equations you're amazing

[@iamadwait]

You are a legend Steve! Take a bow!

[@Justin-rf7md]

Professors should refer to elegant solutions and methods as "sexy" more often. They are. Also; who are the 157 people who disliked this video? Do they not like friendly, enthusiastic, and concise tutorials for circumstantially specific methods of generating solutions for first order ODE's? Probably all University profs chugging that hater-aide.

[@ximena2370]

Thank you, after rewatching your video 3 times and taking good notes, I FINALLYYYY get it! Thank you so much!!

[@CohenRautenkranz]

Excellent job. This topic can be quite perplexing and you laid it out in a clear, concise and, may I say, entertaining manner. Bravo!

[@OliverGomes]

Watched soooo many videos in Differential Eq, until THIS !!! Finally makes sense, Thank you so much !

[@blackpenredpen]

My pleasure!

[@andrewhoban9800]

Great explanation man. Thank you so much. Best quote "Nobody likes negative" Don't worry, be happy!

[@poojanarang2078]

Today I got the actual reason of finding the integrating factor..indeed you have deep knowledge n understanding...looking forward for many such videos!

[@fahimfarhan3806]

I was struggling with integrating factor.Your video was very helpful for me.You have my heartily gratitude. 🌳🌳🌳

[@Sentoefn]

I don't usually comment but this video explained everything to me. I even subscribed. keep it up!

[@jubinraju8165]

The way he those switches markers in his hand between writing is godly

[@berkbuzcu]

Undoubtedly best video on this topic. In the other videos they skip alot of concepts that are hard to explain.

[@dankoch5357]

man, I love you, I just cried tears of joy.

[@muffledd]

thank you so so much! Was learning about this and could not fathom how the product rule was involved. Now I understand it a lot better. Appreciate your work!

[@bilalshahid5831]

Love the explanation! No ambiguity left!

[@asthmen]

“I know this looks very sexy…” Hahaha you have no idea how many times I’ve inadvertently written ‘sex’ instead of ‘secx’… Anyhow, thank you for the explanation! This has helped me a lot.

[@jammcrusader1981]

Don't think this can be explained any better, amazing!

[@s.sradon9782]

Having the lecturer on-screen and all their body language helps me understand the subject. Is it just me?

[@mediterraneanmapping9657]

watching videos helps me learn better, especially for my a levels in 2 weeks

[@manny_k2988]

Im tearing up watching this, everything just fits so perfectly. Thank you

[@blackpenredpen]

Glad to help 😃