No video

Undetermined Coefficients: Solving non-homogeneous ODEs

MY DIFFERENTIAL EQUATIONS PLAYLIST: ► • Ordinary Differential ...
Open Source (i.e free) ODE Textbook: ►web.uvic.ca/~tbazett/diffyqs
How can we solve an ordinary differential equation (ODE) like y''-2y'-3y=3e^2t. The problem is the non-homogeneity on the right hand side. If this was homogeneous and just zero, then previously in our playlist we've studied how to solve constant coefficient homogeneous equations. To deal with the non-homogeneity we use a method called undetermined coefficients. The big idea is to guess a so called particular solution with the same basic form as the right hand side, but with undetermined coefficients. Substitute everything in, and you can solve for the constants in your particular solution. Finally, the general solution is the sum of the homogeneous and the particular solution. I show all the standard guesses and how to deal with situations where there are repeats to the homogeneous in the particular.
0:00 Non-homogeneous ODEs
0:50 Particular vs Homogeneous Solutions
4:00 Finding the Particular Solution
6:45 Second Example
9:15 Chart of standard guesses
11:00 Third Example
OTHER COURSE PLAYLISTS:
►DISCRETE MATH: • Discrete Math (Full Co...
►LINEAR ALGEBRA: • Linear Algebra (Full C...
►CALCULUS I: • Calculus I (Limits, De...
► CALCULUS II: • Calculus II (Integrati...
►MULTIVARIABLE CALCULUS (Calc III): • Calculus III: Multivar...
►VECTOR CALCULUS (Calc IV) • Calculus IV: Vector Ca...
►LAPLACE TRANSFORM: • How to solve ODEs with...
OTHER PLAYLISTS:
► Learning Math Series
• 5 Tips To Make Math Pr...
►Cool Math Series:
• Cool Math Series
BECOME A MEMBER:
►Join: / @drtrefor
MATH BOOKS & MERCH I LOVE:
► My Amazon Affiliate Shop: www.amazon.com/shop/treforbazett
SOCIALS:
►Twitter (math based): / treforbazett
►Instagram (photography based): / treforphotography

Пікірлер: 231

  • @ApoorvSeth
    @ApoorvSeth Жыл бұрын

    These lectures are of great quality and cost me nothing. Thanks to your efforts prof. You are helping many students who either can't afford quality maths education or sometimes have no access to quality education even if they pay.

  • @DrTrefor

    @DrTrefor

    Жыл бұрын

    Glad they are hellping!

  • @mosquito001

    @mosquito001

    10 ай бұрын

    I am suffering from the second. My professors aren't bad, but they don't want to put in the effort after looking how mediocre the rest of my class is, so I have to suffer because of it too

  • @j_gnzz
    @j_gnzz2 жыл бұрын

    I swear this channel explains stuff 10x better than my university's lecture videos actual livesafer

  • @collegemathematics6698

    @collegemathematics6698

    2 жыл бұрын

    I bet you were sleeping during the lecture.

  • @continnum_radhe-radhe

    @continnum_radhe-radhe

    2 жыл бұрын

    @@collegemathematics6698 noo way

  • @hann8528

    @hann8528

    Жыл бұрын

    this is a university topic?… is this the usa 🤣

  • @gabrielreinalter2269

    @gabrielreinalter2269

    Жыл бұрын

    ​@@hann8528 No that isn't just the US it is part of every university course on differential equations. Stop beeing so condescending on the internet, it doesn't make you look smart

  • @Zaryab.khan.Durrani

    @Zaryab.khan.Durrani

    Жыл бұрын

    That too in 10 mins 🗿

  • @bodey609
    @bodey609 Жыл бұрын

    Dr. Trefor Bazett, thank you! After 9 years off maths and going back in to doing a Masters in Engineering this channel has been an absolute blessing. You deserve some serious recognition!

  • @yarenkaya7872
    @yarenkaya78722 жыл бұрын

    I love how even behind a screen you are aiming at teaching the topics by ensuring that your students grasp them, thanks sir

  • @adityamathur5972

    @adityamathur5972

    Жыл бұрын

    good catch

  • @abdullahbabar3439
    @abdullahbabar3439 Жыл бұрын

    Haven't seen anyone delivering the concepts of ODE's better than this . Remarkable methodology.

  • @jamesking2439
    @jamesking24392 жыл бұрын

    I finally understand why any particular solution will work. Thanks! You always make material clear and engaging.

  • @debajyotisg
    @debajyotisg2 жыл бұрын

    This was a great refresher to ODEs. Thanks Dr. Trefor for the wonderful series.

  • @hassamkhan9307
    @hassamkhan9307 Жыл бұрын

    Literally Dr. Trefor, you are the best to help understand mathematics. The beauty of mathematics comes out in your videos!! I am going to make a daily schedule to listen to your videos. Thank you Sir.

  • @wissamboustany3431
    @wissamboustany34312 жыл бұрын

    Really refreshing to feel some enthusiasm while teaching and not just a monotone voice all along. Thanks !

  • @airbender9593
    @airbender95932 жыл бұрын

    Did differential equations 20 or 25 years ago. Make sense watching it 2x speed non-stop. Thank you.

  • @Sughnen
    @Sughnen2 жыл бұрын

    I spent over 10 hours trying to understand this from my school lectures and it only took 13 mins on here. Thanks a lot Trefor, at least I won't be clueless in my exam tomorrow

  • @shargrathdehexen3495
    @shargrathdehexen34952 жыл бұрын

    Thank you so much for your videos! They helped me greatly in passing Differential Equations and made a lot of things that were confusing in lectures really clear and concise! Couldn't have gotten the grade that I did without your extra help.

  • @georgesadler7830
    @georgesadler7830 Жыл бұрын

    Professor Trefor Bazett, thank you for an outstanding video/lecture on Undetermined Coefficients in Ordinary Differential Equations.

  • @debiprasad2646
    @debiprasad26462 жыл бұрын

    The quality of education you are providing is just amazing :) Very helpful , Thank You 🧡

  • @tarunv279
    @tarunv2792 жыл бұрын

    Such crisp presentation! Finally was able to complete my syllabus for ODEs and Lin Algebra

  • @lmyers26
    @lmyers262 жыл бұрын

    You are so so talented at lecturing. Thank you for putting these together!

  • @elliewolcott3240
    @elliewolcott324011 ай бұрын

    Thank you so much for the video! I watched it last year when I took intro to differential equations, and I'm watching it again this year as review for my engineering analysis class. Your explanations are perfect!

  • @DrTrefor

    @DrTrefor

    11 ай бұрын

    You're very welcome!

  • @ankitbasera8470
    @ankitbasera84702 жыл бұрын

    I never really understood why add Complementary Function and Particular Integral but now I do Thanks for clearing a basic concept

  • @yaiba8992
    @yaiba89923 жыл бұрын

    Finally you received after your 7 years of hardwork congrats for 100k

  • @kobedierckx2918
    @kobedierckx2918 Жыл бұрын

    This video about solving linear non homogeneous ODE's is the best on the internet in my opinion, thank you!

  • @bluefenix1457
    @bluefenix1457 Жыл бұрын

    Thank you so much. I wish my proffesor explained with the joy you explain. I'll let you know if I pass my exam in 2 hours

  • @TheFriedAim
    @TheFriedAim9 ай бұрын

    Love this guy, I’ve been confused for a week but not anymore

  • @sodiqoyenuga4997
    @sodiqoyenuga49974 ай бұрын

    I taught I will just watch it and leave it but I found it a great video by great lecturer I need to download it fast.❤ U are too good sir

  • @kalevmccarthy8260
    @kalevmccarthy8260 Жыл бұрын

    Was super confused on this after my lecture. This helped clear it up. Thanks king 👑!!

  • @amitbenjam
    @amitbenjam Жыл бұрын

    And, once again, Trefor managed to make sense of a week worth of lectures in under 13 minuits

  • @bunkydunk7500
    @bunkydunk7500 Жыл бұрын

    I have an ensuing test on this and variation of parameters and these videos are very helpful! Thank you!

  • @raphaelwong8181
    @raphaelwong81812 жыл бұрын

    I have a midterm in two days, and your videos are saving my life!

  • @yangyang8604
    @yangyang86043 жыл бұрын

    Thank you for this series of videos. They help me a lot when trying to study ODEs on my own. Also, the visualizations are very good. I hope there'll be more videos concerning the applications of these equations in real physical cases, like those about mechanical vibrations. After all, thank you for all your works!

  • @DrTrefor

    @DrTrefor

    3 жыл бұрын

    You are most welcome!

  • @thedarklordofcats339

    @thedarklordofcats339

    Жыл бұрын

    The Gigachad submits to his teacher

  • @Jimmy_Hutch
    @Jimmy_Hutch3 жыл бұрын

    Congrats on 100k Dr. Bazett!

  • @DrTrefor

    @DrTrefor

    3 жыл бұрын

    Thanks so much!!!

  • @astro6393
    @astro63932 жыл бұрын

    Nice, you saved me in E&M and now again in another Physics class.

  • @windyjay4627
    @windyjay46273 жыл бұрын

    If i had watched your videos from the start i would be soaring in my DEQ class by now lol. Better late than never i guess as my next exam is in 2 days :,). Thank you so much for everything you are doing!!!!

  • @lesorogolfrancisco8832
    @lesorogolfrancisco8832 Жыл бұрын

    For real the tutorial has a quite elaborate content. Thankyou

  • @adrianstefan1814
    @adrianstefan18143 жыл бұрын

    There is Ate^-t I think 8:21, but it's not a problem. This video is amazing. Very well explained, love your content!

  • @your.studentengagement6077

    @your.studentengagement6077

    2 жыл бұрын

    I was just noticing this and wondered if I made a mistake. thanks for pointing this out. I also believe is a minor error. Video is great.

  • @jeyyviee

    @jeyyviee

    Жыл бұрын

    It took me a 30 mins writing my problem again and again, thinking I made a mistake. Thank you for pointing out.

  • @pras.ku19
    @pras.ku19 Жыл бұрын

    thank u sir for soo much your efforts in explaining the topic in crystal and clear method, i know it is required soo much hardwork in editing and gathering the resources and deliver the best content thanksssss!!!!!

  • @barnabasakinagyonjodetenyleg
    @barnabasakinagyonjodetenyleg Жыл бұрын

    Bro I wish you were my calculus professor here at BME! You make something so complex so easy to understand.

  • @mofiyin9397
    @mofiyin9397 Жыл бұрын

    Thank you so much Dr. Trefor!

  • @ian-hm6cx
    @ian-hm6cx10 ай бұрын

    youre the goat bro my prof is a professional yapper and what you explained in 12 minutes takes him two 50 minute classes

  • @cmdrmo3862
    @cmdrmo3862 Жыл бұрын

    Your videos are wonderful, can't thank you enough

  • @allenhirahara2242
    @allenhirahara22428 ай бұрын

    you are a lifesaver, ty Dr. Trefor~

  • @user-jw8zx1rt5g
    @user-jw8zx1rt5g Жыл бұрын

    thank you so much for this lecture , it is helping me more for my preparation ,thanks again

  • @drkhan462
    @drkhan462 Жыл бұрын

    Good job. I don't remember it being this easy but it looks easy now.

  • @Krishna-gb5ye
    @Krishna-gb5ye2 жыл бұрын

    Thanks sir for your lectures it's really very helpful for me.

  • @mihirrao10
    @mihirrao103 жыл бұрын

    So close to a 100K. Congratulations in advance!

  • @DrTrefor

    @DrTrefor

    3 жыл бұрын

    Haha, thanks!!

  • @day35ofdebuggingthesamelin56

    @day35ofdebuggingthesamelin56

    3 жыл бұрын

    He made it!

  • @gozy2932
    @gozy2932 Жыл бұрын

    This is brilliant. Thank you so much!!!

  • @tac0cat14
    @tac0cat143 жыл бұрын

    Dang I didn’t realize this series is this recently made, do you have an idea when the series will end? These vids are so helpful to follow along while going through the book.

  • @DrTrefor

    @DrTrefor

    3 жыл бұрын

    this exact series is over, but I’m planning more related to ODEs for example Fourier series is next week

  • @anacantu2629
    @anacantu262910 ай бұрын

    Thank you Dr. Trefor

  • @ActuXboxREDAELALAMI
    @ActuXboxREDAELALAMI Жыл бұрын

    Thank you! that was very well explained.

  • @noahgilbertson7530
    @noahgilbertson75302 жыл бұрын

    Oh wow this video gave me a euraka moment, nowhere on the internet has actually explained WHY this works rather than how to use it

  • @Alannnn14
    @Alannnn143 жыл бұрын

    excelent! you have no idea of how much this helps, thx.

  • @DrTrefor

    @DrTrefor

    3 жыл бұрын

    Glad it helped!

  • @mohamedrashad8616
    @mohamedrashad86162 жыл бұрын

    Was so amazing I didnt even blink. Perfect

  • @dannywoyka1203
    @dannywoyka12034 ай бұрын

    really great video, thanks

  • @collegemathematics6698
    @collegemathematics66982 жыл бұрын

    The variation of parameters is more convincing and more general method than undetermined coefficients.

  • @zijianzhang3221
    @zijianzhang32212 жыл бұрын

    It is a really good video, the part which I love so much is the chart part. But I have a question, how to deal the particular solution equation like tcos(t)

  • @annali9577
    @annali95773 жыл бұрын

    This is super helpful, thank you

  • @dumitruenache8480
    @dumitruenache84802 ай бұрын

    man you are a gold mine

  • @HangingQueen
    @HangingQueen10 ай бұрын

    very good explanation

  • @calebstandage4244
    @calebstandage42449 ай бұрын

    Best video I’ve seen on this

  • @tomalabbasi3905
    @tomalabbasi3905 Жыл бұрын

    Great explanation❤❤

  • @timothykorneychuk3353
    @timothykorneychuk33532 жыл бұрын

    Very good video thank you!

  • @HeadRecieverAtHeadOffice
    @HeadRecieverAtHeadOffice Жыл бұрын

    incredible lesson

  • @fahmyahmed4114
    @fahmyahmed41142 жыл бұрын

    Thank you so much for the nice videos, it is really helpful. Right now I am having a problem with the following form: (dv/dt + L1*v = L2*(dx/dt+L3*x)), where t is the time variable, L1, L2, and L3 are constants, dv/dt, and dx/dt are the rate of change of v and x w.r.t time respectively. Is there a possibility to solve it without using Laplace? Is there a generic method to solve similar kinds of problems?

  • @deedatfatahillah7164
    @deedatfatahillah71642 жыл бұрын

    you're a live saver man

  • @mysterioussneha5686
    @mysterioussneha56862 ай бұрын

    that was really helpful!!!

  • @luis_diogo4126
    @luis_diogo4126 Жыл бұрын

    Hi, thank you for the videos, helped me a lot. In the guesses (9:17), the multiplicity shouldn't apply?

  • @YourLocalLeo
    @YourLocalLeo Жыл бұрын

    open source textbook? mvp

  • @frenchfreys
    @frenchfreys Жыл бұрын

    Very helpful!!!

  • @SADDAMHUSSAIN-mw3cv
    @SADDAMHUSSAIN-mw3cv2 жыл бұрын

    Very thank you respected sir...

  • @mangomango5660
    @mangomango5660 Жыл бұрын

    that was so helpful thanks

  • @sulaimonmueezoluwaseun4145
    @sulaimonmueezoluwaseun4145Ай бұрын

    Thanks Dr. It was difficult before I storm this youtube video

  • @charlesrothauser1328
    @charlesrothauser1328 Жыл бұрын

    Ex. 2 highlights the fact that the pieces of the general solution must be linearly independent.

  • @varathannk264
    @varathannk2642 ай бұрын

    Thank you so much sir

  • @vanlang9959
    @vanlang99598 ай бұрын

    thank you for this video sir

  • @muluegebreslasie6312
    @muluegebreslasie63127 ай бұрын

    Hello Dr. Thanks for the lectures, they are really helping to me. I have the ff differential equations and need some ideas on how to start: solve a) x''=-4x^3+4x , b) y''=y^2-y?. Thanks.

  • @adamparker6540
    @adamparker6540 Жыл бұрын

    You are a legend my friend

  • @continnum_radhe-radhe
    @continnum_radhe-radhe2 жыл бұрын

    Thank you very much sir 🔥🔥🔥

  • @ChloeBennett-06
    @ChloeBennett-062 ай бұрын

    Thank you ! 👌

  • @oliviagrill4253
    @oliviagrill42533 жыл бұрын

    First off thank you so much for these videos they’re helping me tremendously. I had a question not super related to this video, but we’re learning variation of parameters right now. Do you have any materials that would help with that or a different way to do questions that ask you to solve using variation of parameters? I’ve looked at other videos and they make some sense but the explanation is too fast and steps are glossed over without explanations.

  • @DrTrefor

    @DrTrefor

    3 жыл бұрын

    I don’t have a video, but check the textbook linked in the description it covers them wrll

  • @oliviagrill4253

    @oliviagrill4253

    3 жыл бұрын

    Thank you so much!

  • @ultranationalistliberalath1195
    @ultranationalistliberalath11952 жыл бұрын

    Sir you definitely deserve more subscribe r.

  • @galdali10
    @galdali10 Жыл бұрын

    Thank you so much 🙏

  • @day35ofdebuggingthesamelin56
    @day35ofdebuggingthesamelin563 жыл бұрын

    Congrats on 100k Subs!

  • @DrTrefor

    @DrTrefor

    3 жыл бұрын

    Thank you so much 😀

  • @bluejaynation137
    @bluejaynation1372 жыл бұрын

    when developing the RHS schema for the Yp by "guessing," how do we check if are schema is correct?

  • @Jasminakanzi
    @Jasminakanzi2 жыл бұрын

    I just wanna say, u are amazing. !!!

  • @aaditya7547
    @aaditya75477 ай бұрын

    Thank you so much

  • @Belinda-qh3xf
    @Belinda-qh3xf10 ай бұрын

    Thank you Prof, you are an awesome teacher

  • @DrTrefor

    @DrTrefor

    10 ай бұрын

    Thank you! 😃

  • @aneeqduraiz4003
    @aneeqduraiz40032 жыл бұрын

    Thank You!

  • @cantorbernoulli4407
    @cantorbernoulli44072 жыл бұрын

    You are a legend thanks

  • @fahrenheit2101
    @fahrenheit21018 ай бұрын

    Aha! I didn't realise that any 2 particular solutions would differ by at most some y_h, that makes so much sense. Finally I can do some well-justified guesswork.

  • @sammywoong3031
    @sammywoong3031 Жыл бұрын

    I LOVE THIS MAN

  • @pepehimovic3135
    @pepehimovic31352 жыл бұрын

    @1:18 by this logic, wouldn’t y_p + an infinite sum of y_h also be a solution? Since y_h will all end up being 0

  • @jacobloufek74
    @jacobloufek742 жыл бұрын

    Thank you!

  • @RoryMacKinnon-wx6ye
    @RoryMacKinnon-wx6ye8 ай бұрын

    Dr. Trefor... The God head... Thank you for sharing your knowledge, it does so much.

  • @ashu5587
    @ashu55872 жыл бұрын

    Thank you!!!

  • @user-wt8vz3lp9u
    @user-wt8vz3lp9u4 ай бұрын

    Thank you sir

  • @elgatito00
    @elgatito003 жыл бұрын

    OMG I needed this video! 🥳🥳

  • @DrTrefor

    @DrTrefor

    3 жыл бұрын

    Glad it helped!

  • @selfstudypk
    @selfstudypk3 жыл бұрын

    Perfect as usual.

  • @DrTrefor

    @DrTrefor

    3 жыл бұрын

    thank you!

  • @steveboege9195
    @steveboege9195 Жыл бұрын

    Thanks!

  • @Tavo88Spurs
    @Tavo88Spurs2 жыл бұрын

    wow you just explained calculus in laymans terms...huge thanks.

  • @ogunsadebenjaminadeiyin2729
    @ogunsadebenjaminadeiyin27293 жыл бұрын

    Excellent.

  • @erikawimmer7908
    @erikawimmer79083 жыл бұрын

    Hey Trefor! I have got a question that I can find no answer to and since you are a math Professor I hope you can help me. Its about partial differential equations (i know not exactly the topic of the video) in physics. My question is: How can we be sure that ,since we often can only find parts of the general solution of a pde, that this part represents the physical scenario? An example to clear things up: take for example the schrödinger equation. We usualy solve it by seperation of variables. However there are defenetly other solutions as well that are not seprable but still solve the equation, we just cant find them analitically. How can we then still make sure that the studied particle has the wave function (or one of the wave functions) that is/are given by the seprable solutions we found and not by another? Doesnt that basically destroy or chance of getting information abou the particle since the most general solutions to pdes are usualy such a wider class? Thanks in advance!

  • @DrTrefor

    @DrTrefor

    3 жыл бұрын

    Definitely look up the various existence and uniqueness results for separable PDEs, this is what ultimately gives us a handle on the “halting problem” you describe.

  • @erikawimmer7908

    @erikawimmer7908

    3 жыл бұрын

    @@DrTrefor Thank you!

  • @slimknight_
    @slimknight_2 жыл бұрын

    you deserve more subscribers