Second Order Linear Differential Equations
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- เผยแพร่เมื่อ 2 ต.ค. 2024
- 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-tuto...
Full-Length Videos and Worksheets:
/ collections
Final Exams and Video Playlists: www.video-tutor.net/
Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections
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!
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.
hahaha exactly!
just curious, what university do you attend?
Very correct
Ditto. He explains it much better than any uni tutorial.
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!
*while
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 :(
I am still a student, but hopefully I want to donate these gentlemen some money!
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dear school teachers stop skipping steps and start telling us both the how and why! like this guy in the video!!
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They run out time doing that that what schooling does but education takes time hahaha.
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We hate school
hey, you dropped this 👑
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....
-6r*
Yes it really threw me off
can we pin this off
@@lich3622 is correct
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
This 25 minutes covered a two and a half lecture that I didn’t even understand...Thanks a lot♥️
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
@@NativeGatekeeper101 I’m so sorry. I can’t understand a single thing you said.
@@lasithathilakarathne3205 For this level we need to speak at least 2 languages. In Europa, some people speak 3 and 4 language Plus Mathematics language.
@@NativeGatekeeper101 that’s true
same, but i feel my teacher translate this lecture wrongly.
On questions 2,3, should it not be in the form ay''+by'+cy? Instead of ay''+by'+c?
👍👍👍
yeah, this was confusing me, too.
I was thinking the same
This man has saved me countless hours by actually being able to teach the subject. Thank you so much
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
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.
My 3rd year of general physics and still watch yours and Houston maths prep videos you two are legends
Previous video: “fraction”
me: *presses upgrade*
This video: “SECOND-ORDER SEPERABLE DIFFERENTIAL EQUATION”
me: *GO BACK GO BACK!!*
actually these are second order linear homogenous ordinary differential equations, they are not separable.
Seperables are when you can cross multiply....these are linear homogenous
My vision is to be a great maths teacher 1 day. You are a stepping stone. Thanks alot man.
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
Thanks for helping me increase my confidence. You patiently explain incredibly well.
At 6:59, shouldn't this 9 be 9y? And similarly at 9:00, shouldn't the 16 be 16y?
I think so either... sir.
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
Honestly, thank you so much for this! You are carrying me through my maths module at uni
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.
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
i was thinking of it too.
No problemo. So long as you are proficient with manipulation of algebraic expressions.
You are the best lecturer ever. You need an award. In lecture time this would have cost me around £400
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 ❤
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.
Your teaching style of explaining th material then immediately going into practice problems is great! Thank you!
I'm so happy I came across this channel! Learned a lot in these 25 mins
Thank God I read this comment otherwise I would have forgotten to put the playback speed on 2x
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)
My professor basically just gace me a book and told me to figure everything out on my own... thank god for youtube
you're a great teacher and i love your teaching style
Thank you sir! Mas natututo ako sa inyo kesa sa instructor namin na puro pagawa lang alam.
At 7:01 it should be 9y instead of 9
and 9:11 should be 16y instead of 16
and 12:58 should be 25y instead of 25
@@kolemakinde No bro, you should understand the word "Order" of differential equation, it's different
@@lies4212 no no @Kole Makinde is right
dude you clearly dont understand the subject
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.
At 7:00 shouldn't the equation be 9y, not just 9. Same thing at 9:05, it should be 16y not 16. If you are talking about homogeneous equations.
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!
calc 2????? I just started doing this in calc 4
hey bro ,(9:20) for 9y'' +24y' +16 =0 ,isn't it a none-Homogeneous equation for the constant "16 " ,or you mean "16y " instead.
Yeah I think he did it again in the y"+8y'+25=0 one.It has to be 25y otherwise you cannot use the e^rx when you plug it in as a solution and then come up with the ar^2+br+c=0
Great video tho.Helped me understand the topic.
yeah i just noticed that too
He did the same thing w the problem immediately after with y''+8y'+25 = 0
Hi there. One thing I don't understand is why the solution-set carry's an x for the second solution Ce^rx + CXe^rx . This seem to happen while there is only one solution for r. But in the cases where the quadratic formula gives you two solutions there is no x in the solution. Do you have a video where you explain this ?? Thank you for the video it was great and helped me understand everything except for this.
0:14 when he says ''you might want to have a sheet of paper with you to take down some notes'' i felt this was gonna be hard
Thanks so much for the video, but I'm kinda confused. In the second example y'' -6y'+9=0, 9 isn't a y term so how was the formula still able to work
I am also confused at that part
This is a mistake and I’m sure he just solved it with 9y instead of just 9
Thank you very much, I was also asking myself the exact same question..
Couldn't have been a better time for posting! Thank you so much! You have helped a lot!
Quick question - when you started doing the example problems, shouldnt they all be ay''+by'+cy+d=0? It seems you're missing just the normal y variable after all your constants, or else the ar^2+br+c eqn doesn't really make sense. Am I mistaken?
i am also wondering the same thing!!!!!
Great video but most of your example equations have a slight mistake: they are in the form of ay'' + by' + c = 0, not ay'' + by' + cy = 0. Doesn't matter though, i still understood the topic
Thank you so much sir, this is probably the best channel I've ever come across.
good video. clear enough for me to understand,thank you
I'm watching you since over a year
and I reached 4:06 but still didn't understand from you are you solving the example or are you giving a general formula.
this is first time i get confused from you
but still u r the best
THIS IS THE VIDEO THAT FINALLY MADE ME UNDERSTAND
9:11 it has to be 9y''+24y'+16y=0, the y term is missing for coefficient 16.
Good video but for some of the examples given in this video (minutes 8 and 9), you forgot to add the "y" for the last term.
Literally understood more within 5 minutes of watching this vid than an hour of lectures.
For the first example for case 3, how do you get the two values of Beta as 3? Why is it not + & - 3? Also thank you so much for this channel!
in the second example, a 'y' must be attached to the '9' in the given equation to end up with a c value of 9 in the 'r' equation, no? The equation shown would be non-homogeneous.
3rd example does this as well
it seems many of the examples do this. correct me if I'm wrong but believe this is a big mistake.
On the second example, did he forget to put y on 9 or you can still use quadratic equation even if 9 is only 9 and not 9y?
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.
Itni achi english kese ho saktiye
amen
Stop trying to sound smart
This comment belongs in a museum.
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.
Hi, at 7:10 can I still consider c=9 even if it is only 9 rather than 9y in the original equation ? Sorry I am being picky but I don’t want to make any mistakes during the exam so
i was thinking the same thing and i think there should be a y
You have saved me a lot of time and effort thanks a lot!
Idk What to say but Sir you are the best!
😭
Clarity is clear to see
Beautifully explained, thank you.
Thank u from EGYPT .
Its amazing video❤
You are the best. Thanks for simplifying
Wonderful I have learned how to deal with such order differential equations superb
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!
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big mistake in the video... The general solution are valid only for a y''+b y'+cy=0 not a y''+b y' +c=0
OCT is not only helping students. helping some teachers as well
Notice he used or defined y as equals to the infamous e^(rx)
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!!
Nice explanation thanks
Thanks a lot 😊 great video 📸
Thanks for excellent teaching.
Thank you dear teacher
You're a godsend!
for the second and third problem, shouldn't it be 9y and 16y instead of just 9 and 16 ?
*same issue for the problems later on
Thank you. Very helpful tutorial...
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!
Make a playlist for differential equations please
Bro keep it up love from india🙏🙏🙏
thank you for this awesome video
07:01 the sample questions you gave from about 7 mins to 16 minutes are non homogeneous, so I don't think the same approach for homogeneous equations will apply
But how is that general solution derived?
(Is there any other video of yours for the derivation of it?)
unfortunately, you gotta learn it on the textbook. This video is only for someone who wanna pass their test and forget all about it right after. No offense😂
25 minutes better than 3 hours of lecture. Thanks a lot
Well explained
People!! Did he just taught us solving differential equations in such an easy and beautiful way such that we're not going to forget it in this life??!
about the y'' - 6y' + 9, we dont have y =e^rx on 9, how do we factor out the e^rx
Thank you from sri lanka
In examples 2 and 3, should there be a y next to the last constant in the starting equation? Otherwise, you can't use ay''+by'+cy=0 (from my understanding)
I have the same question, but the chances of him answering are very low
After 10 minutes of the video how did he use the characteristic equation there isnt a y next to the 16 so it isnt a homogenous equation
And the equation after it he did the same is their anything that im not knowing right
So I've been doind them and if that was the case with no y next to the 16 it would be another solution as it's not homogenous therefore I think he just made a mistake, cos without it and y=exp(rx) you wouldn't get the form ar^2+br+c=0
It is a 2nd order homogeneous DE. That Dude explained better than my professor.
yeah you known that xp
Thank you for speaking English, my professor fails to speak in a language that students can understand
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
Ever so clear!
Well explained
Thanks alot!!!
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
idk how my prof rambles for an hour and i still dont get it but i’m only 1 min and 44 secs into this video and i already understand
the initial equations had "Y" but your next examples didn't and you just used the same formula.... you made a mistake or i missedsomething?? can some one help please?
i want to ask the same thing
If there was TH-cam when I studied university, I would score higher in mathematics than I did; simply because I would follow your highly instructive videos rather than attending boring lectures.
Can you do some tutorials on laplace transform please.