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

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  • Опубліковано 29 лис 2024

КОМЕНТАРІ • 620

  • @AC-vj3iy
    @AC-vj3iy 7 років тому +896

    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 6 років тому +16

      *20 mins

    • @GhostyOcean
      @GhostyOcean 5 років тому +12

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

    • @BradleyCopp
      @BradleyCopp 5 років тому +48

      2* speed for the pros of studying

    • @lanlanyiyiyi3933
      @lanlanyiyiyi3933 5 років тому +2

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

    • @aga080
      @aga080 5 років тому +4

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

  • @andreguimaraes9347
    @andreguimaraes9347 7 років тому +179

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

  • @fawazalkhelaiwi2525
    @fawazalkhelaiwi2525 7 років тому +380

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

  • @aquienpuedaimportar3028
    @aquienpuedaimportar3028 6 років тому +129

    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 років тому +16

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

    • @thefunpolice
      @thefunpolice 11 місяців тому

      Exactly right. Spot on comment.

  • @NMelakis1
    @NMelakis1 6 років тому +24

    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!

  • @okechukwuciano4997
    @okechukwuciano4997 Місяць тому +2

    My favorite UA-cam 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.

  • @fatsquirrel75
    @fatsquirrel75 7 років тому +119

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

  • @TheodorRiegger
    @TheodorRiegger Місяць тому +3

    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 ❤

  • @ridpathos7821
    @ridpathos7821 6 років тому +224

    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 5 років тому +12

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

    • @itsmesuryat7570
      @itsmesuryat7570 4 роки тому +11

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

    • @vinaykumar2030
      @vinaykumar2030 4 роки тому +6

      and this is how teaching should be done

    • @jrddvs24
      @jrddvs24 4 роки тому +4

      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 роки тому +2

      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
    @jazzm5557 7 років тому +51

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

  • @fullmetalpotato1258
    @fullmetalpotato1258 6 років тому +26

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

  • @BAEX2013G
    @BAEX2013G 4 роки тому +11

    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!

  • @elvinjafarli6257
    @elvinjafarli6257 7 років тому +165

    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 років тому +2

      yeah, i feel you bro. same shit in ubc

    • @TheTck90
      @TheTck90 5 років тому +2

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

    • @abrahamverbo3855
      @abrahamverbo3855 5 років тому +10

      You guys are paying?

    • @ceciliagai79
      @ceciliagai79 5 років тому +1

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

    • @parthasur6018
      @parthasur6018 3 роки тому +3

      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.

  • @raffaellucaschumann8365
    @raffaellucaschumann8365 7 років тому +17

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

  • @aymankhan7905
    @aymankhan7905 3 роки тому +4

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

  • @zasgat
    @zasgat 5 років тому +65

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

  • @collegeguy1325
    @collegeguy1325 6 років тому +4

    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

  • @senya9299
    @senya9299 4 роки тому +6

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

    • @mohsenhca
      @mohsenhca 4 роки тому

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

  • @FlavorWorld
    @FlavorWorld 6 років тому +28

    blackpenredpen is saving my grade!

  • @thefunpolice
    @thefunpolice 11 місяців тому +1

    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.

  • @sumeirkhinda3166
    @sumeirkhinda3166 5 років тому +28

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

  • @IamFated
    @IamFated 10 місяців тому +1

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

  • @lukahnapeirogon8197
    @lukahnapeirogon8197 6 років тому +6

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

  • @ammar.a2950
    @ammar.a2950 3 роки тому +4

    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
    @wontpower 8 років тому +3

    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  8 років тому +2

      Will Power thank you. Exact equations will be next!

  • @em22beats28
    @em22beats28 4 роки тому

    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

  • @tpstrat14
    @tpstrat14 4 роки тому +1

    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!

  • @yognaughty
    @yognaughty 5 років тому +1

    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.

  • @dong8912
    @dong8912 6 років тому +1

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

  • @JENNY9767
    @JENNY9767 6 років тому +3

    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!

  • @Maria_farah
    @Maria_farah Місяць тому

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

  • @asotayousafzai
    @asotayousafzai 4 роки тому

    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.

  • @mciniell
    @mciniell Рік тому +1

    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!

  • @infinitymfg5397
    @infinitymfg5397 8 років тому +42

    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.

  • @MRZEE-nf1fq
    @MRZEE-nf1fq Рік тому +1

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

  • @Coggernautt
    @Coggernautt 7 років тому

    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
      @blackpenredpen  7 років тому

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

  • @gaurav1319
    @gaurav1319 2 роки тому +6

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

  • @JSSTyger
    @JSSTyger 7 років тому

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

  • @aferolkay
    @aferolkay 5 років тому

    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.

  • @noahpritchard4214
    @noahpritchard4214 5 років тому

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

  • @azwadrahman4796
    @azwadrahman4796 6 років тому +3

    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!

  • @83zn
    @83zn 4 роки тому

    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.

  • @sammelnik586
    @sammelnik586 5 років тому +1

    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
    @bwfir3ball 6 років тому +1

    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!

  • @hexman89
    @hexman89 6 років тому +3

    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!!

  • @Siddhantabora
    @Siddhantabora 5 років тому +1

    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

  • @vinaykumar2030
    @vinaykumar2030 4 роки тому +1

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

  • @rokurosora2404
    @rokurosora2404 6 років тому

    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.

  • @leenaadil8474
    @leenaadil8474 2 роки тому +1

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

  • @priscilladoran9545
    @priscilladoran9545 3 роки тому

    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!

  • @teebiz8694
    @teebiz8694 4 роки тому +1

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

  • @EmergedLocket0
    @EmergedLocket0 6 років тому +1

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

  • @aga080
    @aga080 5 років тому

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

  • @Chamorizard
    @Chamorizard 6 років тому

    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 !

  • @NWSCS
    @NWSCS 7 років тому +1

    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
    @vincentcarlen4052 4 роки тому

    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 :)

  • @siennawire4976
    @siennawire4976 6 років тому

    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!

  • @OliverGomes
    @OliverGomes 7 років тому

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

  • @danielclipper931
    @danielclipper931 3 місяці тому

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

  • @lindyn4
    @lindyn4 4 роки тому

    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

  • @zoom-jx3so
    @zoom-jx3so 5 років тому +1

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

  • @agginswaggin
    @agginswaggin 5 років тому +2

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

  • @devenjain7116
    @devenjain7116 4 роки тому +2

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

    • @mohsenhca
      @mohsenhca 4 роки тому

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

  • @joluju2375
    @joluju2375 5 років тому

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

  • @the_martian_45
    @the_martian_45 6 років тому

    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!

  • @sethholland1157
    @sethholland1157 6 років тому

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

  • @Festus2022
    @Festus2022 3 роки тому

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

  • @fahimfarhan3806
    @fahimfarhan3806 3 роки тому

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

  • @jemcel0397
    @jemcel0397 8 років тому +1

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

  • @paulkimivanramirez9468
    @paulkimivanramirez9468 3 роки тому

    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.

  • @shaharyar4093
    @shaharyar4093 3 роки тому

    Your better than every professor I've ever had

  • @lexsonsamson94
    @lexsonsamson94 7 років тому +1

    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

  • @AliBarisa
    @AliBarisa 11 місяців тому +1

    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

  • @stavem8864
    @stavem8864 5 років тому +1

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

  • @tomatrix7525
    @tomatrix7525 3 роки тому

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

  • @CohenRautenkranz
    @CohenRautenkranz 6 років тому

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

  • @poojanarang2078
    @poojanarang2078 4 роки тому

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

  • @michaelgurnick8422
    @michaelgurnick8422 3 роки тому

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

  • @ximena2370
    @ximena2370 6 місяців тому

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

  • @berkbuzcu
    @berkbuzcu 6 років тому

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

  • @manny_k2988
    @manny_k2988 2 роки тому +1

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

  • @mediterraneanmapping9657
    @mediterraneanmapping9657 7 років тому

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

  • @masoncamera273
    @masoncamera273 3 роки тому

    Reverse chain rule made it so much more clear to me

  • @Sentoefn
    @Sentoefn 4 роки тому +1

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

  • @Jamelele
    @Jamelele 7 років тому

    15:02
    best explanation ever why we use the positive version of sec(x)

  • @bilalshahid5831
    @bilalshahid5831 5 років тому +1

    Love the explanation! No ambiguity left!

  • @Justin-rf7md
    @Justin-rf7md 3 роки тому +2

    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.

  • @dankoch5357
    @dankoch5357 4 роки тому

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

  • @MiHwAr2149
    @MiHwAr2149 3 роки тому

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

  • @jammcrusader1981
    @jammcrusader1981 4 роки тому

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

  • @eternaldreamerofsleep
    @eternaldreamerofsleep 4 місяці тому

    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

  • @duanerackham9567
    @duanerackham9567 5 років тому

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

  • @muffledd
    @muffledd 7 місяців тому

    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!

  • @andrewhoban9800
    @andrewhoban9800 5 років тому

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

  • @myfatherwillhearaboutthis7621
    @myfatherwillhearaboutthis7621 Місяць тому

    You're my favorite math youtuber

  • @abbiecarter-dawson7834
    @abbiecarter-dawson7834 6 років тому +2

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

  • @Royce133c
    @Royce133c 10 місяців тому +1

    This video is a god send, thank you

  • @iamadwait
    @iamadwait 5 років тому +1

    You are a legend Steve! Take a bow!

  • @Cashias_clay
    @Cashias_clay 6 років тому +2

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

  • @johannbauer2863
    @johannbauer2863 5 років тому

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