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

Learn how to solve a first-order linear differential equation with the integrating factor approach.
Verify the solution: • Q143
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Thank you so much!
Fake Product Rule (Math for fun): • fake derivative produc...
Diff Eq Playlist: • Playlist

Пікірлер: 603

  • @AC-vj3iy
    @AC-vj3iy6 жыл бұрын

    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

    @masterdon187

    5 жыл бұрын

    *20 mins

  • @GhostyOcean

    @GhostyOcean

    5 жыл бұрын

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

  • @BradleyCopp

    @BradleyCopp

    5 жыл бұрын

    2* speed for the pros of studying

  • @lanlanyiyiyi3933

    @lanlanyiyiyi3933

    4 жыл бұрын

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

  • @aga080

    @aga080

    4 жыл бұрын

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

  • @fawazalkhelaiwi2525
    @fawazalkhelaiwi25256 жыл бұрын

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

  • @user-en5vj6vr2u

    @user-en5vj6vr2u

    4 жыл бұрын

    heyyy sec(x)y ;)

  • @real_dddf

    @real_dddf

    3 жыл бұрын

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

  • @AdityaKumar-gv4dj

    @AdityaKumar-gv4dj

    4 ай бұрын

    sec C 😂

  • @YusufSuleiman-kk6fu

    @YusufSuleiman-kk6fu

    3 ай бұрын

    😅😂​@@AdityaKumar-gv4dj

  • @andreguimaraes9347
    @andreguimaraes93477 жыл бұрын

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

  • @blackpenredpen

    @blackpenredpen

    7 жыл бұрын

    NicE!

  • @frankpyapao6499

    @frankpyapao6499

    2 ай бұрын

    Of course

  • @ridpathos7821
    @ridpathos78215 жыл бұрын

    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

    @aga080

    4 жыл бұрын

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

  • @itsmesuryat7570

    @itsmesuryat7570

    3 жыл бұрын

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

  • @vinaykumar2030

    @vinaykumar2030

    3 жыл бұрын

    and this is how teaching should be done

  • @jrddvs24

    @jrddvs24

    3 жыл бұрын

    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

    @tomatrix7525

    3 жыл бұрын

    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.

  • @zasgat
    @zasgat4 жыл бұрын

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

  • @aquienpuedaimportar3028
    @aquienpuedaimportar30286 жыл бұрын

    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

    @blackpenredpen

    6 жыл бұрын

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

  • @thefunpolice

    @thefunpolice

    7 ай бұрын

    Exactly right. Spot on comment.

  • @NMelakis1
    @NMelakis16 жыл бұрын

    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
    @fatsquirrel756 жыл бұрын

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

  • @blackpenredpen

    @blackpenredpen

    6 жыл бұрын

    Great to hear! Thanks!!!!

  • @postnubilaphoebus96

    @postnubilaphoebus96

    4 жыл бұрын

    Blackpenredpen - click for clicks

  • @elvinjafarli6257
    @elvinjafarli62576 жыл бұрын

    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

    @WA-hq6ls

    5 жыл бұрын

    yeah, i feel you bro. same shit in ubc

  • @TheTck90

    @TheTck90

    5 жыл бұрын

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

  • @abrahamverbo3855

    @abrahamverbo3855

    4 жыл бұрын

    You guys are paying?

  • @ceciliagai79

    @ceciliagai79

    4 жыл бұрын

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

  • @parthasur6018

    @parthasur6018

    3 жыл бұрын

    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.

  • @timdodge8178
    @timdodge81784 жыл бұрын

    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!

  • @jazzm5557
    @jazzm55577 жыл бұрын

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

  • @blackpenredpen

    @blackpenredpen

    7 жыл бұрын

    Jazz M you're welcome!

  • @aymankhan7905
    @aymankhan79053 жыл бұрын

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

  • @fullmetalpotato1258
    @fullmetalpotato12586 жыл бұрын

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

  • @blackpenredpen

    @blackpenredpen

    6 жыл бұрын

    Fallout Nick thank you!!

  • @thefunpolice
    @thefunpolice7 ай бұрын

    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.

  • @FilibertoRafaelZuritaAbad
    @FilibertoRafaelZuritaAbad6 жыл бұрын

    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 !

  • @mciniell
    @mciniell Жыл бұрын

    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!

  • @ammar.a2950
    @ammar.a29503 жыл бұрын

    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!!

  • @JENNY9767
    @JENNY97676 жыл бұрын

    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!

  • @noahpritchard4214
    @noahpritchard42145 жыл бұрын

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

  • @gaurav1319
    @gaurav13192 жыл бұрын

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

  • @siennawire4976
    @siennawire49766 жыл бұрын

    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!

  • @sammelnik586
    @sammelnik5865 жыл бұрын

    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!

  • @collegeguy1325
    @collegeguy13256 жыл бұрын

    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

  • @FlavorWorld
    @FlavorWorld6 жыл бұрын

    blackpenredpen is saving my grade!

  • @blackpenredpen

    @blackpenredpen

    6 жыл бұрын

    Glad to help!!!!!

  • @senya9299
    @senya92993 жыл бұрын

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

  • @mohsenhca

    @mohsenhca

    3 жыл бұрын

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

  • @CohenRautenkranz
    @CohenRautenkranz5 жыл бұрын

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

  • @lukahnapeirogon8197
    @lukahnapeirogon81976 жыл бұрын

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

  • @sumeirkhinda3166
    @sumeirkhinda31665 жыл бұрын

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

  • @blackpenredpen

    @blackpenredpen

    5 жыл бұрын

    : )))

  • @em22beats28
    @em22beats283 жыл бұрын

    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

  • @asotayousafzai
    @asotayousafzai4 жыл бұрын

    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.

  • @nicholasmartin6353
    @nicholasmartin63536 жыл бұрын

    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!

  • @azwadrahman4796
    @azwadrahman47966 жыл бұрын

    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!

  • @sethholland1157
    @sethholland11576 жыл бұрын

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

  • @IamFated
    @IamFated6 ай бұрын

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

  • @vincentcarlen4052
    @vincentcarlen40524 жыл бұрын

    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 :)

  • @Festus2022
    @Festus20223 жыл бұрын

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

  • @michaelgurnick8422
    @michaelgurnick84223 жыл бұрын

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

  • @JakkalsJack
    @JakkalsJack6 жыл бұрын

    Thank you very much! Great video and very easy to understand on the way you explained it!

  • @lexsonsamson94
    @lexsonsamson946 жыл бұрын

    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

  • @bwfir3ball
    @bwfir3ball5 жыл бұрын

    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!

  • @raffaellucaschumann8365
    @raffaellucaschumann83657 жыл бұрын

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

  • @blackpenredpen

    @blackpenredpen

    7 жыл бұрын

    My pleasure!

  • @Animalkingdom.x

    @Animalkingdom.x

    2 жыл бұрын

    i tell you

  • @muffledd
    @muffledd3 ай бұрын

    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!

  • @hexman89
    @hexman895 жыл бұрын

    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!!

  • @NWSCS
    @NWSCS7 жыл бұрын

    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!!!

  • @yognaughty
    @yognaughty5 жыл бұрын

    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.

  • @grey8116
    @grey81165 жыл бұрын

    This is a great video. Very well explained and really helped on this topic. Thanks for posting.

  • @TheDissapearingGuy
    @TheDissapearingGuy6 жыл бұрын

    Great video, thanks dude! I was stuck on these types of problems for ages but since I watched your video it seems so simple! Keep up the good work :)

  • @ioannaathineos5269
    @ioannaathineos52695 ай бұрын

    amazing way of teaching and approaching the mathematical concepts! Thank you!

  • @teebiz8694
    @teebiz86944 жыл бұрын

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

  • @jemcel0397
    @jemcel03977 жыл бұрын

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

  • @vinaykumar2030
    @vinaykumar20303 жыл бұрын

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

  • @tpstrat14
    @tpstrat144 жыл бұрын

    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!

  • @jialingzhou4311
    @jialingzhou43115 жыл бұрын

    Awesome video! You made the whole thing a lot more easier. Thank you so much!

  • @dong8912
    @dong89126 жыл бұрын

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

  • @Animalkingdom.x

    @Animalkingdom.x

    2 жыл бұрын

    ❤❤

  • @wontpower
    @wontpower7 жыл бұрын

    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

    @blackpenredpen

    7 жыл бұрын

    Will Power thank you. Exact equations will be next!

  • @lindyn4
    @lindyn44 жыл бұрын

    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

  • @priscilladoran9545
    @priscilladoran95453 жыл бұрын

    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!

  • @ximena2370
    @ximena23703 ай бұрын

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

  • @ryd-er-die6697
    @ryd-er-die66974 жыл бұрын

    Great video...thank you for making it it...it was so much clearer than my textbooks examples of the integrating factor method

  • @joluju2375
    @joluju23754 жыл бұрын

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

  • @dianaal-qassim3348
    @dianaal-qassim33487 жыл бұрын

    Thank you so much! I was having a difficulty understanding this, but after watching this video, I totally understood the idea, and I am amazed. Thank you :)

  • @miramontesapril89
    @miramontesapril892 жыл бұрын

    You kept me sane; today at least! I did not understand my class’s lecture today and you totally saved me

  • @zoom-jx3so
    @zoom-jx3so5 жыл бұрын

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

  • @EmergedLocket0
    @EmergedLocket05 жыл бұрын

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

  • @poojanarang2078
    @poojanarang20784 жыл бұрын

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

  • @jammcrusader1981
    @jammcrusader19814 жыл бұрын

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

  • @83zn
    @83zn4 жыл бұрын

    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.

  • @Siddhantabora
    @Siddhantabora4 жыл бұрын

    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

  • @stavem8864
    @stavem88645 жыл бұрын

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

  • @rokurosora2404
    @rokurosora24046 жыл бұрын

    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.

  • @user-xl1ig1bn6i
    @user-xl1ig1bn6i7 ай бұрын

    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

  • @abbiecarter-dawson7834
    @abbiecarter-dawson78346 жыл бұрын

    this video has helped me out enormously, thank you so much!

  • @fahimfarhan3806
    @fahimfarhan38063 жыл бұрын

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

  • @murilopalomosebilla2999
    @murilopalomosebilla29994 жыл бұрын

    Great explanation! The best one I have seen.

  • @JSSTyger
    @JSSTyger7 жыл бұрын

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

  • @blackpenredpen

    @blackpenredpen

    7 жыл бұрын

    JSSTyger thank you.

  • @tomatrix7525
    @tomatrix75252 жыл бұрын

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

  • @leenaadil8474
    @leenaadil84742 жыл бұрын

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

  • @OliverGomes
    @OliverGomes7 жыл бұрын

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

  • @blackpenredpen

    @blackpenredpen

    7 жыл бұрын

    My pleasure!

  • @eternaldreamerofsleep
    @eternaldreamerofsleep24 күн бұрын

    Damn, thank you so much. I really liked seeing the process of how the formula was derived instead of just memorizing it, very cool and interesting

  • @Cashias_clay
    @Cashias_clay5 жыл бұрын

    Great work, my professors should definitely take some tips from you.

  • @Alfonzo6000000
    @Alfonzo60000003 жыл бұрын

    Thank you for your great teaching! I understand it way better than when my professor taught it!

  • @duanerackham9567
    @duanerackham95674 жыл бұрын

    You explained this so well. I actually understand what's going on now

  • @berkbuzcu
    @berkbuzcu5 жыл бұрын

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

  • @user-yp8ui7lq7q
    @user-yp8ui7lq7q5 жыл бұрын

    Thanks mate. This video is really useful and easy to understand!

  • @shanzshuhong1023
    @shanzshuhong10234 жыл бұрын

    Thank you so much!! Your explanation in this video is extremely clear and MUCH MORE helpful than the videos provided by my school. Keep it up and hope to see more videos!!

  • @mohsenhca

    @mohsenhca

    3 жыл бұрын

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

  • @chenadam6339
    @chenadam63395 жыл бұрын

    detailed explanation for complex questions! thank you!

  • @georgesadler7830
    @georgesadler7830 Жыл бұрын

    Thank you for the video on solving Linear Differential Equations.

  • @johannbauer2863
    @johannbauer28635 жыл бұрын

    Woah, this is so cool and mindblowing, I watched this 1 year ago and forgot it, so I came back :D

  • @redballs
    @redballs6 жыл бұрын

    2 thumbs up! Thank you for taking the time to explain thoroughly

  • @aga080
    @aga0804 жыл бұрын

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

  • @roshanpatel4037
    @roshanpatel40373 жыл бұрын

    nice job dude you make math so enjoyable

  • @andrewmarabante4548
    @andrewmarabante45484 жыл бұрын

    Great video man. Thorough explanation

  • @saran3855
    @saran38557 жыл бұрын

    Yes! Thank you, very clear and easy to understand ( i learned more in that 20mins than 1hr in my lecture) . I look forward to watching your other videos!

  • @blackpenredpen

    @blackpenredpen

    7 жыл бұрын

    I am very happy to hear! Cheers!

  • @infinitymfg5397
    @infinitymfg53977 жыл бұрын

    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

    @blackpenredpen

    7 жыл бұрын

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

  • @habakukmurigi1651

    @habakukmurigi1651

    2 жыл бұрын

    😂😂😂

  • @cosmaschikhutu5128
    @cosmaschikhutu51286 жыл бұрын

    The presentation is very helpful for i am getting better understanding of some concepts

  • @nesivapama
    @nesivapama4 жыл бұрын

    This is just brilliant! You saved me a lot of time understanding this concepts. BTW, I love DE.

  • @khiramanimurmu9021
    @khiramanimurmu90216 жыл бұрын

    Great video!! Thanks for explaining the logic behind "Integrating Factor" 😃😃

  • @lawrancesim4299
    @lawrancesim42993 жыл бұрын

    You are really a life savior man! Thanks a lot.

  • @Mustoccoli1
    @Mustoccoli15 жыл бұрын

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

  • @luizmiranda6213
    @luizmiranda62137 жыл бұрын

    you rock men!!! even in new year you still working. Happy new year. May god bless every step you make, every video, your wise and fun microfone, you family! love ya, peace!!! =]

  • @blackpenredpen

    @blackpenredpen

    7 жыл бұрын

    THANK YOU! Happy new year to you as well!!!