Undetermined Coefficients: Solving non-homogeneous ODEs
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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
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Пікірлер: 231
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
Жыл бұрын
Glad they are hellping!
@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
I swear this channel explains stuff 10x better than my university's lecture videos actual livesafer
@collegemathematics6698
2 жыл бұрын
I bet you were sleeping during the lecture.
@continnum_radhe-radhe
2 жыл бұрын
@@collegemathematics6698 noo way
@hann8528
Жыл бұрын
this is a university topic?… is this the usa 🤣
@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
Жыл бұрын
That too in 10 mins 🗿
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!
I love how even behind a screen you are aiming at teaching the topics by ensuring that your students grasp them, thanks sir
@adityamathur5972
Жыл бұрын
good catch
Haven't seen anyone delivering the concepts of ODE's better than this . Remarkable methodology.
I finally understand why any particular solution will work. Thanks! You always make material clear and engaging.
This was a great refresher to ODEs. Thanks Dr. Trefor for the wonderful series.
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.
Really refreshing to feel some enthusiasm while teaching and not just a monotone voice all along. Thanks !
Did differential equations 20 or 25 years ago. Make sense watching it 2x speed non-stop. Thank you.
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
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.
Professor Trefor Bazett, thank you for an outstanding video/lecture on Undetermined Coefficients in Ordinary Differential Equations.
The quality of education you are providing is just amazing :) Very helpful , Thank You 🧡
Such crisp presentation! Finally was able to complete my syllabus for ODEs and Lin Algebra
You are so so talented at lecturing. Thank you for putting these together!
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
11 ай бұрын
You're very welcome!
I never really understood why add Complementary Function and Particular Integral but now I do Thanks for clearing a basic concept
Finally you received after your 7 years of hardwork congrats for 100k
This video about solving linear non homogeneous ODE's is the best on the internet in my opinion, thank you!
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
Love this guy, I’ve been confused for a week but not anymore
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
Was super confused on this after my lecture. This helped clear it up. Thanks king 👑!!
And, once again, Trefor managed to make sense of a week worth of lectures in under 13 minuits
I have an ensuing test on this and variation of parameters and these videos are very helpful! Thank you!
I have a midterm in two days, and your videos are saving my life!
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
3 жыл бұрын
You are most welcome!
@thedarklordofcats339
Жыл бұрын
The Gigachad submits to his teacher
Congrats on 100k Dr. Bazett!
@DrTrefor
3 жыл бұрын
Thanks so much!!!
Nice, you saved me in E&M and now again in another Physics class.
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!!!!
For real the tutorial has a quite elaborate content. Thankyou
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
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
Жыл бұрын
It took me a 30 mins writing my problem again and again, thinking I made a mistake. Thank you for pointing out.
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!!!!!
Bro I wish you were my calculus professor here at BME! You make something so complex so easy to understand.
Thank you so much Dr. Trefor!
youre the goat bro my prof is a professional yapper and what you explained in 12 minutes takes him two 50 minute classes
Your videos are wonderful, can't thank you enough
you are a lifesaver, ty Dr. Trefor~
thank you so much for this lecture , it is helping me more for my preparation ,thanks again
Good job. I don't remember it being this easy but it looks easy now.
Thanks sir for your lectures it's really very helpful for me.
So close to a 100K. Congratulations in advance!
@DrTrefor
3 жыл бұрын
Haha, thanks!!
@day35ofdebuggingthesamelin56
3 жыл бұрын
He made it!
This is brilliant. Thank you so much!!!
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
3 жыл бұрын
this exact series is over, but I’m planning more related to ODEs for example Fourier series is next week
Thank you Dr. Trefor
Thank you! that was very well explained.
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
excelent! you have no idea of how much this helps, thx.
@DrTrefor
3 жыл бұрын
Glad it helped!
Was so amazing I didnt even blink. Perfect
really great video, thanks
The variation of parameters is more convincing and more general method than undetermined coefficients.
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)
This is super helpful, thank you
man you are a gold mine
very good explanation
Best video I’ve seen on this
Great explanation❤❤
Very good video thank you!
incredible lesson
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?
you're a live saver man
that was really helpful!!!
Hi, thank you for the videos, helped me a lot. In the guesses (9:17), the multiplicity shouldn't apply?
open source textbook? mvp
Very helpful!!!
Very thank you respected sir...
that was so helpful thanks
Thanks Dr. It was difficult before I storm this youtube video
Ex. 2 highlights the fact that the pieces of the general solution must be linearly independent.
Thank you so much sir
thank you for this video sir
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.
You are a legend my friend
Thank you very much sir 🔥🔥🔥
Thank you ! 👌
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
3 жыл бұрын
I don’t have a video, but check the textbook linked in the description it covers them wrll
@oliviagrill4253
3 жыл бұрын
Thank you so much!
Sir you definitely deserve more subscribe r.
Thank you so much 🙏
Congrats on 100k Subs!
@DrTrefor
3 жыл бұрын
Thank you so much 😀
when developing the RHS schema for the Yp by "guessing," how do we check if are schema is correct?
I just wanna say, u are amazing. !!!
Thank you so much
Thank you Prof, you are an awesome teacher
@DrTrefor
10 ай бұрын
Thank you! 😃
Thank You!
You are a legend thanks
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.
I LOVE THIS MAN
@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
Thank you!
Dr. Trefor... The God head... Thank you for sharing your knowledge, it does so much.
Thank you!!!
Thank you sir
OMG I needed this video! 🥳🥳
@DrTrefor
3 жыл бұрын
Glad it helped!
Perfect as usual.
@DrTrefor
3 жыл бұрын
thank you!
Thanks!
wow you just explained calculus in laymans terms...huge thanks.
Excellent.
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
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
3 жыл бұрын
@@DrTrefor Thank you!
you deserve more subscribers