Second Order Linear Differential Equations

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  • Опубликовано: 24 ноя 2019
  • This Calculus 3 video tutorial provides a basic introduction into second order linear differential equations. It provides 3 cases that you need to be familiar with. It explains how to find the general solution of the differential equation as well as how to solve the initial value problem and the boundary value problem.
    Lines & Planes - Intersection:
    • How To Find The Point ...
    Angle Between Two Planes:
    • How To Find The Angle ...
    Distance Between Point and Plane:
    • How To Find The Distan...
    Chain Rule - Partial Derivatives:
    • Chain Rule With Partia...
    Implicit Partial Differentiation:
    • Implicit Differentiati...
    ________________________________
    Directional Derivatives:
    • How To Find The Direct...
    Limits of Multivariable Functions:
    • Limits of Multivariabl...
    Double Integrals:
    • Double Integrals
    Local Extrema & Critical Points:
    • Local Extrema, Critica...
    Absolute Extrema - Max & Min:
    • Absolute Maximum and M...
    ________________________________
    Lagrange Multipliers:
    • Lagrange Multipliers
    Triple Integrals:
    • Triple Integrals - Cal...
    2nd Order - Differential Equations:
    • Second Order Linear Di...
    Undetermined Coefficients:
    • Method of Undetermined...
    Variation of Parameters:
    • Variation of Parameter...
    ________________________________
    Final Exams and Video Playlists:
    www.video-tutor.net/
    Full-Length Videos and Worksheets:
    / collections

Комментарии • 560

  • @TheOrganicChemistryTutor
    @TheOrganicChemistryTutor  6 месяцев назад +8

    Final Exams and Video Playlists: www.video-tutor.net/
    Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections

  • @thunderbolt997
    @thunderbolt997 3 года назад +688

    dear school teachers stop skipping steps and start telling us both the how and why! like this guy in the video!!

    • @uniqueideas3112
      @uniqueideas3112 3 года назад +4

      👍👍👍

    • @pvpetvlogs5298
      @pvpetvlogs5298 3 года назад

      Yeah true 😊

    • @mary.s.v
      @mary.s.v 3 года назад

      Yeeeeeessss😢

    • @Theabok853
      @Theabok853 2 года назад +5

      They run out time doing that that what schooling does but education takes time hahaha.

    • @lifelyrics5659
      @lifelyrics5659 2 года назад

      Haha yeahhhh
      We hate school

  • @AiZeno
    @AiZeno 4 года назад +643

    not gonna lie, this 25 mins video = 2 lecture classes of 2 hour = 4 hours of lecture and is paid. Whilst this is free. You deserve something better!

    • @gartyqam
      @gartyqam 3 года назад +1

      *while

    • @alisonlaett9625
      @alisonlaett9625 3 года назад +7

      I'm kinda jealous. My teacher covered this and more in one 1h15min lecture. I wish we were able to go at slower pace, but that would only be possible if the university added a lecture period every week, which they won't do :(

    • @anindyaroy5692
      @anindyaroy5692 3 года назад +4

      I am still a student, but hopefully I want to donate these gentlemen some money!

    • @marybean2231
      @marybean2231 3 года назад +10

      @@gartyqam you're so cool

    • @fahimally3923
      @fahimally3923 3 года назад

      TRUEEE TRUEEE TRUEEEEE

  • @blakkermambaa
    @blakkermambaa 3 года назад +598

    You should be getting my tuition instead of my university. I've learned more physics, chemistry, and calculus from you these last few years than I have from most classes. Thanks!

    • @alexmiller1148
      @alexmiller1148 3 года назад +20

      Agree! Students like us learn more from you than in university classes. We just really enrolled 'coz we don't really wanna be left out.

    • @mikayjd
      @mikayjd 3 года назад +2

      hahaha exactly!

    • @radhikakamdar5556
      @radhikakamdar5556 Год назад +3

      just curious, what university do you attend?

    • @stephenefeamos6721
      @stephenefeamos6721 Год назад

      Very correct

    • @GryffieTube
      @GryffieTube 10 месяцев назад +1

      Ditto. He explains it much better than any uni tutorial.

  • @lasithathilakarathne3205
    @lasithathilakarathne3205 3 года назад +274

    This 25 minutes covered a two and a half lecture that I didn’t even understand...Thanks a lot♥️

    • @NativeGatekeeper101
      @NativeGatekeeper101 3 года назад +1

      Tienes que escribir cada concepto que el diga..paso por paso..Cuando usar cuadratic formula y cuando debes usar factorizacion..Recuerda DOS SOLUCIONES -PRIMER CASO . UNA SOLUCION_SEGUNDO CASO. Tercer caso imaginarios numeros etc

    • @lasithathilakarathne3205
      @lasithathilakarathne3205 3 года назад

      @@NativeGatekeeper101 I’m so sorry. I can’t understand a single thing you said.

    • @NativeGatekeeper101
      @NativeGatekeeper101 3 года назад +1

      @@lasithathilakarathne3205 For this level we need to speak at least 2 languages. In Europa, some people speak 3 and 4 language Plus Mathematics language.

    • @lasithathilakarathne3205
      @lasithathilakarathne3205 3 года назад

      @@NativeGatekeeper101 that’s true

    • @mohammed_ghazali
      @mohammed_ghazali 3 года назад

      same, but i feel my teacher translate this lecture wrongly.

  • @rmdir
    @rmdir Год назад +71

    I appreciate how you dive quickly into actually solving problems, rather than getting bogged down in theory. At times the theory is important, but most of the time we just need to get straight down to business. In the long run, this no-nonsense format is more useful than any other math tutor on youtube.

  • @Jadester
    @Jadester 3 года назад +57

    You are such a hero man. Seriously I can't think you enough, your generosity in sharing all this knowledge in such a compelling way genuinely makes me want to cry. You have helped me so much in my college classes, thank you.

  • @paranoidcomet
    @paranoidcomet 3 года назад +47

    hey, you dropped this 👑

  • @virajgorthi7488
    @virajgorthi7488 3 года назад +95

    For Case 3, one tip my professor gave us was to solve by completing the square for the quadratic, then square rooting the function on both sides. It's a lot easier and gives you the same answer as the quadratic formula

    • @richieescarola9529
      @richieescarola9529 2 года назад +1

      i was thinking of it too.

    • @user-xl1ig1bn6i
      @user-xl1ig1bn6i 6 месяцев назад

      No problemo. So long as you are proficient with manipulation of algebraic expressions.

  • @sijaladnani4765
    @sijaladnani4765 2 года назад +15

    I'm here right now because I wanted to thank you personally, Mr. Organic chemistry tutor. The clarity of your videos, with your heartfelt yet joyful tone, brings tears to my eyes. I am but a mortal vessel, and as such, I am unable to adequately articulate the sense of divinity and celestial dominance your video explanations have bestowed upon me. The whim and astonishment that each soul touching connection left is enough to stimulate the previously sluggish flow of deep emotions that have lied in the depths of my soul after my university lectures. Thank you very much, Mr. Organic chemistry tutor for your beautiful explnantions.

  • @Kgt743
    @Kgt743 3 года назад +14

    This man has saved me countless hours by actually being able to teach the subject. Thank you so much

  • @baps04
    @baps04 7 месяцев назад +18

    5:07 - Case 1 Example
    6:53 - Case 2 Example
    8:45 - Case 2 Example
    12:50 - Case 3 Example
    16:28 - Case 3 Example (with initial values)
    21:22 - Case 2 Example (with boundary values)

  • @lynnroach731
    @lynnroach731 3 года назад +35

    I love that these videos always explain each step, even stuff learned in previous math classes. I'm doing this in calc 2 right now, but I always get rusty on factoring polynomials when I haven't done it in a while, but whenever he explains it I feel like it all comes back. My professor would probably just say that we learned this in Int. Algebra which is true but we can't always remember everything off the top of our heads!

    • @tcv_sacred734
      @tcv_sacred734 8 месяцев назад

      calc 2????? I just started doing this in calc 4

  • @HeyKevinYT
    @HeyKevinYT 4 года назад +177

    Previous video: “fraction”
    me: *presses upgrade*
    This video: “SECOND-ORDER SEPERABLE DIFFERENTIAL EQUATION”
    me: *GO BACK GO BACK!!*

    • @AB-gu9ui
      @AB-gu9ui 4 года назад +15

      actually these are second order linear homogenous ordinary differential equations, they are not separable.

    • @tomatrix7525
      @tomatrix7525 4 года назад +2

      Seperables are when you can cross multiply....these are linear homogenous

  • @georgesadler7830
    @georgesadler7830 Год назад +8

    Professor Organic Chemistry Tutor, thank you for an awesome video/lecture on Second Order Linear Differential Equations. Second Order Linear Differential Equations are simple to follow and understand provided that students have taken Calculus I and II. Thanks to the viewers for finding and correcting the error/errors in this video.

  • @nahomfekadu1375
    @nahomfekadu1375 2 года назад +44

    It was very good tutorial but i have a doubt starting from example 2 which is like
    y''-6y'+9=0
    r^2-6y=0 not r^2-6y+9=0 (the question is given 9 not 9y but you're working the calculation as it were 9y.)
    make a correction sir....

    • @lich3622
      @lich3622 2 года назад +3

      -6r*

    • @macsentiffany618
      @macsentiffany618 2 года назад +9

      Yes it really threw me off

    • @alihoussa2238
      @alihoussa2238 2 года назад +6

      can we pin this off

    • @AbdiBedaso
      @AbdiBedaso Год назад +1

      @@lich3622 is correct

    • @crimsonflood1643
      @crimsonflood1643 3 месяца назад +6

      oh I'm glad I'm not the only one, this really threw me off and had me doubting everything I knew, yeah this was a bad mistake on his part

  • @Da_Muncher
    @Da_Muncher 2 года назад +13

    Your videos have saved me so much time especially a night before my exam. I have been watching you for years and I appreciate you for spreading the knowledge to all of us in such a simple way.

  • @jessnunn
    @jessnunn Год назад +26

    On questions 2,3, should it not be in the form ay''+by'+cy? Instead of ay''+by'+c?

  • @crimsonglory7823
    @crimsonglory7823 2 года назад +3

    I can't thank you enough for all the help you've given to students all over the world. Not all heroes wear capes, some tutor people on RUclips.

  • @ArchitMoharir
    @ArchitMoharir Год назад

    You know you are doing a great job when the video is still being used after 3 years !!
    Thank you so much

  • @beautyoflifebeautyoflife762
    @beautyoflifebeautyoflife762 3 года назад +6

    you are the reason why I am getting great grades in my engineering classes and maths can be quite difficult for me to understand. Wish you were my tutor. You are AWESOME!

  • @vincentprado9981
    @vincentprado9981 Год назад +12

    I was so confused. He made a few mistakes. To get a C, the term should have a y in it. It can't stand alone. Like for 9y''+24y'+16=0. In order to get the solution that he got, he actually solved 9y''+24y'+16y=0

  • @lewismackenzie7484
    @lewismackenzie7484 3 года назад +10

    Honestly, thank you so much for this! You are carrying me through my maths module at uni

  • @kevincui5282
    @kevincui5282 Год назад +3

    We spent an entire week on this one topic at my university and I didn't learn crap, yet after this 25 minute video I just breezed through all the homework! Thank you!

  • @NativeGatekeeper101
    @NativeGatekeeper101 3 года назад +13

    Thanks for helping me increase my confidence. You patiently explain incredibly well.

  • @Hell.on.foot1
    @Hell.on.foot1 Год назад +2

    My 3rd year of general physics and still watch yours and Houston maths prep videos you two are legends

  • @brendanpaget2914
    @brendanpaget2914 4 года назад +1

    Couldn't have been a better time for posting! Thank you so much! You have helped a lot!

  • @artousi
    @artousi 8 месяцев назад

    The legend continues...Best engineering RUclips channel there is. No matter what I am trying to learn this guy has a video for it that is guaranteed to make me understand it better than I would from class.

  • @armzeeth5706
    @armzeeth5706 4 месяца назад

    Your concise 25-minute lecture was as impactful as a lengthy 4-hour session. I truly appreciate your clear explanations, Chief. Not only you cover engineering mathematics comprehensively, but you also addressed our entire semester's modules. Thank you for your invaluable contribution! 🙏❣️

  • @justinsauve808
    @justinsauve808 Год назад

    Your teaching style of explaining th material then immediately going into practice problems is great! Thank you!

  • @fosterasiedu1212
    @fosterasiedu1212 4 года назад +3

    Have been waiting forever. Thank you. More of differential calculus.

  • @adrianocordba
    @adrianocordba Год назад +4

    Just wow, Mr. you should be really proud of what you represent for som many students. Your platform is gives so much hope to people all around the world, each one of your videos is a step closer to our goals. Thank you so very much and Merry Christmas, Professor.

  • @youcancallmeal7272
    @youcancallmeal7272 3 года назад +1

    Indescribably helpful, pretty sure you are literally the best teacher in the universe.

  • @kapishmalik
    @kapishmalik Год назад +2

    This 25 min lecture came in clutch for my exam in 6 hours , thanks a lot.

  • @bigbrainsvoid1560
    @bigbrainsvoid1560 3 года назад

    I've been procrastinating for hours thinking this is the hardest thing ever but u explaining anything makes it so easy ty so much

  • @glen2551
    @glen2551 3 года назад

    Seriously this lecture is one of the best of all the maths program i follow on youtube, you deserve to be paid sir
    evey step was well understood

  • @tark3822
    @tark3822 2 года назад +5

    25 minutes better than 3 hours of lecture. Thanks a lot

  • @mkmathstutorials6645
    @mkmathstutorials6645 2 года назад +2

    My vision is to be a great maths teacher 1 day. You are a stepping stone. Thanks alot man.

  • @andro7306
    @andro7306 4 года назад +2

    you're a great teacher and i love your teaching style

  • @_MarSify_
    @_MarSify_ 3 года назад +7

    you are a life saver man :') i could not understand this in 2 lectures but you made it easy peasy in a 25min video omg , can't thank you enough

  • @1unga
    @1unga 2 года назад +2

    This was perfectly explained, thank you so much!

  • @CNCentriccreations
    @CNCentriccreations Год назад +8

    You have saved me a lot of time and effort thanks a lot!

  • @warwick802
    @warwick802 9 месяцев назад +1

    I pay old professors who should be retired thousands of dollars to show up to class and watch them teach nothing/overcomplicate everything
    This gentleman teaches me what I need to know for free and I can view it at my pace. Amazing times we live in

  • @sholaibukun1352
    @sholaibukun1352 Год назад +2

    Wow😮, this is mind blowing . You were able to streamline this explanation into about 25 min 16sec . I have been looking through my materials for hours and couldn’t get any reasonable solution to the question I was pose at.
    Thanks 🙏 a lot sir

  • @simrankapoor7712
    @simrankapoor7712 3 года назад

    Thank you so much sir, this is probably the best channel I've ever come across.

  • @Bk_official003
    @Bk_official003 Год назад +2

    I really appreciate your help thanks a lot I have been struggling with that two whole days not doing anything else. Thanks a lot brother

  • @JohnnyMontilla
    @JohnnyMontilla Год назад +1

    YOU SAVED MY GRADE! THANK YOU!

  • @cynthiamonkap9910
    @cynthiamonkap9910 Год назад +1

    you make differential equation so easy, thank you so much for boosting my exam confidence

  • @user-lz3rb9jy3o
    @user-lz3rb9jy3o 6 месяцев назад +1

    good video. clear enough for me to understand,thank you

  • @MrKristian252
    @MrKristian252 2 года назад +4

    I had Differential Equations last year, and it has been a big black hole in by brain.
    Thank you so much for filling in those gaps!!

  • @danielxbox28
    @danielxbox28 Год назад

    Man , This guy is literally saving me for my Diff equations test tomorrow!. I'm understanding clearly with the combinations of lots of examples and a bit of theory. The professors just give you abstract theory , which doesn't help me understand on it's own!

  • @zacharycornman977
    @zacharycornman977 8 месяцев назад

    Thanks so much for making these things so much simpler to understand man.

  • @ADARSHTSRA
    @ADARSHTSRA 3 года назад +1

    Beautifully explained, thank you.

  • @anwan5
    @anwan5 2 года назад +2

    Thank you so freakin much! You help me understand and learn much more than my "professors", you made me like math again :)

  • @MShazarul
    @MShazarul 4 года назад +4

    Just in time! Final is nearing and your first order differential helps a ton! Thanks (I haven't watch the full video but I know it's gonna rock my paper!)

  • @mikayjd
    @mikayjd 3 года назад

    Watching for my exams tomorrow. Learned a lot. Thanks!

  • @mariecolquhoun6181
    @mariecolquhoun6181 3 года назад

    You are the best lecturer ever. You need an award. In lecture time this would have cost me around £400

  • @mr.electro4674
    @mr.electro4674 8 месяцев назад +1

    Had a lecture on these today, took rigorous notes, looked at the problem sheet and came straight here 😂, i know you always got me covered bro, thank you

  • @almustaphaumar2904
    @almustaphaumar2904 10 месяцев назад

    Thank you for the most simple explanation

  • @AlEx-ro7kd
    @AlEx-ro7kd 3 года назад

    ive been putting off learning this cuz it sounded so hard but u explained it perfectly

  • @marcellacella8293
    @marcellacella8293 2 года назад

    Thankyou for the clear explation, it helps me a lot

  • @lauraoliveira9679
    @lauraoliveira9679 8 месяцев назад +1

    College professors should learn from you because in 15 minutes you made me understand the topic and idea 10 better than sitting through 2 lectures did.

  • @coltonlittlewood7085
    @coltonlittlewood7085 2 года назад

    You explain this so much better than my professor. I love you

  • @adamiennd8167
    @adamiennd8167 4 года назад +8

    I'm from Romania, but the first time when i will travel to America I will give u more beers than u can drink. Thank you. I'm first university year and u save my math exam! RESPECT FROM ROMANIA

  • @waanochannel6502
    @waanochannel6502 4 года назад +1

    On time man ❤💖❤ i appreciate it. Keep uploading these stuff bro.

  • @rithuvarshana.t6822
    @rithuvarshana.t6822 11 дней назад

    Very Great Video for studying Second order ODE's This is what exactly i liked about it after 4 years also it's worth watching man

  • @okotphiliphs14
    @okotphiliphs14 Год назад

    you are t the best tutor ever. your channel has helped me alot in my studies.

  • @rusirubatuwatta8731
    @rusirubatuwatta8731 3 года назад +2

    Thank you! Now i can finish my assignment ❤️

  • @manzidaniel5814
    @manzidaniel5814 2 года назад

    Thanks a lot tutor, this is well explained way better than the lecturers in collage.

  • @zanginapeterwinnimi4370
    @zanginapeterwinnimi4370 Год назад

    He explains the concept for students' understanding.thanks alot.

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    @fgbnh2946 Год назад

    Thank you so much for all of your videos, it has been a great help!!!, I am going to do well in my exam because of you!!!!!

  • @ayandajoemunikwa7722
    @ayandajoemunikwa7722 Год назад

    You are the best. Thanks for simplifying

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    @dramaqueen9475 3 года назад

    i literally am in love with u. where tf would i be without ur videos?

  • @bluegreyfictions
    @bluegreyfictions 10 месяцев назад

    thank you so much for such easier explanation.

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    @pitbullman925 2 года назад

    thank you so much, you made my FE exam review understandable.....your a gift from heaven

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    @devgey1518 4 года назад

    very good very good , this is very assuring. sometimes one feels lonely, however a hero comes to the rescue. that hero is you

  • @notpiccaboo142
    @notpiccaboo142 3 года назад

    Thank you so much, our professor sux!!! Esp this time of quarantine where online classes are conducted.

  • @haythem4866
    @haythem4866 2 года назад

    I appreciate when people explain like him rather than writing Ancient Greek on the board and expecting us to understand from the get go.

  • @rachel_k8519
    @rachel_k8519 3 года назад +11

    I'm so happy I came across this channel! Learned a lot in these 25 mins

    • @jordabox
      @jordabox 3 года назад +1

      Thank God I read this comment otherwise I would have forgotten to put the playback speed on 2x

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    @ejoshtech5358 2 года назад

    U the god of math tutorials, simply unmatched.
    If you had programming tutorials you would be the almighty

  • @tbow2912
    @tbow2912 3 года назад

    Excellent video! Well explained.

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    @nellymuthoki8743 2 года назад

    Your voice always heal my hearts mathematical problems 😇👩‍🎓🙏

  • @hourglas9836
    @hourglas9836 Месяц назад

    Thank you so much Sir this 25 minutes class was equal to a 4 hours lecture that i didn't even understood, I'm very grateful ❤

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    @abbyhinson9106 3 года назад +1

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    This vids really help me. Keep up the amazing work!

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    @kayssobih 4 года назад +1

    You are a true legend keep the excellent work👍🏼👌🏻

  • @robertherd4579
    @robertherd4579 3 года назад

    Thnx for ur tutorials mate. Kudos ❤️🙏

  • @cryptobossz
    @cryptobossz Год назад

    Best channel I ever see in my Life 🙇🙇🙇🙇

  • @otabeksaibnazarov5704
    @otabeksaibnazarov5704 2 года назад +1

    thank you for lesson, now I can solve Second order linear differential equations

  • @dianaprinceislel.6827
    @dianaprinceislel.6827 3 года назад

    This 25 minute video sums up all the stuffs in my 19-page module, I can't understand a thing in it until I watched this video.

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    @allenhirahara2242 7 месяцев назад

    You are a lifesaver, thank you~

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    @ahmednabil776 3 года назад

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  • @Da007Prince
    @Da007Prince 4 года назад

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    @edungdivinefavour6977 Год назад

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    @dulapiip 3 года назад

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    @effieleonard7172 3 года назад

    This channel helped me a lot! thanks

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    @faisalkaka2840 3 года назад +1

    Hi
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  • @thoraskey5402
    @thoraskey5402 Год назад

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    @aimanimtiaz1066 3 года назад

    one of the amazing teacher in the world

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    @richieescarola9529 2 года назад

    Thank you for saving my life.

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    @zarrinnahid448 3 года назад +1

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