/ professorleonard Exploring Initial Value problems in Differential Equations and what they represent. An extension of General Solutions to Particular Solutions.
Me too! I just spent an hour trying to work out what I did wrong. I thought, “How did I get C=3? I did something wrong!” Until I looked at the comments 😂
I whitelisted the channel but I hate the ads so much because they're about getting a tutor or using a website with tutorials. I already have Professor Leonard!!
@4:00 shouldn't C be equal to 3? When you enter 1/3, still is a good solution for the differential equation. 3 works as well i think. Feel free to double check.
Yea I Was doing the example and got C = 3 and kept going back over the video to see if I messed up but it became apparent I Was right. Ty for the comment Prof you can edit videos now maybe add a fix in?
It is indeed a solution. In fact, any value of c works, that's why it's called an *arbitrary* constant. However, we want that particular value of c that makes y(x) go through (0, 3) and that's c = 3.
I have watched lecture videos from various different universities like MIT and Stanford and I have to say your videos are much better. You are a great professor. Out of all my math professors from algebra up to calc 3 and linear algebra I have only had 1 professor that was in your league. Unfortunately he moved colleges after I took him for calc 2. I will be taking Diff EQ in the fall of this year, but first I am watching all of your videos. Definitely going to get an A :) Thanks for your help.
You have a way of pre-empting and heading off points of misunderstanding before they happen. Makes the learning process so smooth. I love your teaching style!
Thank you so much for creating these videos. I'm taking diffiQ this semester and didn't realize how much I relied on your videos to get me through. I'm a broke college student now but I'll be sure to pay it forward once I graduate. I truly appreciate these lectures!
Professor Leonard you are a talented teacher, and may I say a god of maths. You know how to give us the informations and stress on the important stuff we need to know so that we can solve any problem we get with 0 difficulties. Your way of teaching is never boring I could watch all of your playlists in one time like I'm watching some kind of fun series. It's because of you that I passed Calc 1 and 2 and now hopefully Differential equations. No other teacher has ever done this they make maths look like a boring and hard subject. You have my respect. God bless you proff
I totally raise my hand. I think it's almost gotten me in trouble, when I was watching his lecture in public (I think people thought I was doing a nazi salute or something :D )
@@marka.1770 For real. I'm not a nazi, though, in case anyone is wondering (and I'm not directing this at you, Mark). It's such a shame that anyone would need to clarify that.
21:00. Even with the initial condition y(0) = 1. There will still be a family of solutions because C = pi/4 + k * pi where k is an integer. It might be nice to add 0 < C < 1 to the question. That ensures C = pi/4 is the only correct answer.
I love this guy!!!! I’ve been watching him since trig. Now I’m in Diffy Q and I am confident due to him. My professors at my school speak in another language. Thank the gods for you Leonard!! Oh and go 9ers!
You are a very good professor. Honestly, My mind was blown up with Differential but then I found your this series, going through it and it is easy now.
I hope you see this. I really wanted to tell you that you made this concept so simple!!! I am going to go through all your stuff!! I a taking a Masters course over ODE’s and I feel like they are speaking Greek! You helped me out so much!! Thank you!!!
Though "snuck" has become more common, "sneaked" is the proper verb; as it is the past tense of "sneak." "Snuck" is a vulgarity that will be the end of the English language according to my English professor. Haha!
Thanks for the great videos! Much faster getting through the material sans classroom. At minute 7:32 you cancelled out a -Ce^-x with another -Ce^-x. In order for them to cancel one of them has to be +Ce^-x. You only needed to cancel the +x with the -x. Thanks!
Really the solution that pass through x=0 when y=3 is 1/0.33333... e^2x not 1/3 e^2x. Which means that the constant is already 1/0.3333... = 3 not 1/3. The mistake in your calculations is done when you assume that in 3 = C.1 you can pass 3 below 1, when really what the equality is telling you is that you already hace C = 3
You are the best teacher I have seen. I feel better now when I see you are teaching Differential Equations. I passed from Calculus 3 because of your help and thanks a lot for that. Can you please also add the subtopics name (as written on the book) in the information part such as "separable equation, exact equation or numerical method" ?
Thank you so much for this. Currently taking diffy q online and my instructor doesn't give any type of lecture notes/videos. Luckily I have your videos! haha
It's important to check that the general solution _is_ a solution because on the test, showing it's a solution will be worth a chunk of the points, or your professor may slip in a non-solution to trip you up. More pragmatically, the whole point of the course, in the end, is to be able to find these solutions yourself. This is Differential Equations, not Advanced Derivative Exercises. Proposing a solution is only going to be a fraction of the credit if you don't show it's the correct solution. It's a bit like derivatives and integrals were the arithmetic, and now Diff Eq is the algebra that lets us solve for unknowns.
2:48 Another value for C would be 5pi/4, since the period of tangent is pi. Also because tangent is positive in both the first and third quadrant. This means that what you said is not fully correct, but only partially. But please, feel free to correct me if I’m wrong. Nevertheless, I really enjoy your videos and I’m currently watching your entire series for differential equations to learn how to solve them. Thanks for the help.
So helpful to us the students of mathematics but seeing c=1/3 made me think that I am following a fine art prof but thanks that you realized the mistake.
Hi Professor Leonard, here I am watching this for calculus 2. Your videos are amazing and very straightforward. Would you consider to make videos about Introduction to Linear algebra? :) Thank you! Keep up the good work!
Just a thank you on saving my exam that is literally tomorrow and I am in deep deep shit. You are a beckon of hope on getting at least a C (maximum a C?)
Maybe im missing something but for the last example i solved it the same way but i noticed that 4y''=y are not equal when i sub. Every example they had to equal. Maybe he just used that example to show that r could be two different numbers only. My question is could 1/2 still be a solution even if the original equations dont equal each other
@@subhranshusonamoni I actually came to the comment section to confirm that C is in fact 3 and that I'm not missing anything so thank you Ashraf Owaida
