Differential Equations: Lecture 2.3 Linear Equations

[@sueton1797]

This is how a person should teach something. Some fun here, some serious stuff there. Thanks for making this lecture public!

[@emrongardizi7252]

0 dislikes for a reason. don't know how I would pass my DE class without this channel

[@TheMathSorcerer]

❤️

[@hernanvsyt]

Minute 18:44 : y=-xcos(x)+Cx

[@SobechukwuDi-Ibor]

thank you i was hecka confused

[@centralprocessingunit2564]

Your lectures are so good. I'm in high school and I had no knowledge or clue about what you did in these videos, but after watching on 2 of your lectures I can actually follow along!!!! so strong

[@TheMathSorcerer]

Wow that is so good!! Learning this stuff in high school is so awesome, you rock!!

[@luiginumbers6268]

Same here, although by now you must be pretty far along in college!

[@koenth2359]

9:30 For me feels much easier just to realise that a negative power is 1 over a positive power, so e^-ln|x| = 1/e^ln|x| = 1/|x|

[@shaniceshipp9016]

Thanks for helping me learn Differential Equations during the pandemic.

[@TheMathSorcerer]

you are welcome!

[@aldominicgatlabayan6925]

I've been watching his videos for sometime now since I started college, and I know many of his students already LOL. Hi Rafael and Anna. thank you sir, you made online learning a lot easier for me from the Philippines

[@redandgreenchristmasblues23]

you are an exceptional teacher! its so pleasant to hear laughter and see a smile during a lecture. you breaking it down into steps and demonstrating is very helpful!! :D

[@baron5432]

I am a junior in college taking this class and your lectures are very clear and easy to follow. Thank you for all the help.

[@lybakamran9019]

Thank you so much for saving my life by explaining in such a nice way! May god bless you Sirr!!

[@TheMathSorcerer]

Happy to help!

[@sinuouslocks]

You are a gift from God! Muchisimas gracias, no sabe cuanto le agradezco que est`e subiendo estos videos.

[@TheMathSorcerer]

Gracias❤️

[@ashleyosorio9513]

I love your channel. It has been helping me out a lot. Thank you so much!!

[@JohnFL]

Same here!

[@mathiasjeppesen6781]

I am from Denmark, and I am in 10th grade! These lectures are really interesting and I am enjoying watching them!

[@mathiasjeppesen6781]

I have watched Calc 1, Calc 2 and now I am beginning to watch these lectures

[@saidalmaqbali3832]

at the beginning of this semester I was so confused , but now I found my Salvador

[@TheMathSorcerer]

👍

[@JohnFL]

Thank You, Math Sorcerer! I was confused with the mu(x) term, but with your enjoyable explanation and the option to pause the lecture (which I can't do in class), I think I understand it better now. Also, I like how you threw in some made-up trivia about the letter mu, being based off the English alphabet instead of the other way around 🙃🐴

[@shiminglu3940]

thanks for making the integrating method more clear than textbook : )

[@Guineafloof]

i ltrly love you so much! THANK YOU!!! - all the way from kuwait

[@sihambelmiloud3351]

This is the best channel if you want to become a true mathematician

[@TheMathSorcerer]

:)

[@jonathancontreras9632]

I love this guys laugh 😂

[@FidiasAlejandre]

GOAT fr fr bruh no cap bro

[@sm1522]

Around 30:18 what happened to the C of integration ??

[@robn2497]

I understand the process and I understand what I call the reverse product rule step. Small question when computing the u(x) = e^(intergral(-1/x dx)) the answer given is e^(ln(1/x)). WHERE did the constant go like should the answer not be e^(ln(1/x)+c) => e^(ln(1/x)*e^(constant) ???

[@brandonbennett4970]

I also have this question. Did you end up finding an answer?

[@lemonlime8041]

Since in the next step you multiply the whole DE by mu(x) you can just divide the whole DE by e^(constant) which gives you the same result

[@heleni5946]

At 28:46, why is there an additional du in the integration? isn't it just -du/u?

[@valor36az]

First time I understand what the integration factor represents, thank you.

[@TheMathSorcerer]

You are welcome!

[@nonamenosurname6127]

if I am not mistaken I'm watching your 4th lecture and I have already remembered names of your students ;)

[@TheMathSorcerer]

Awesome lol

[@iremiposiajayi122]

First question: in the first example, can’t we just put the x’s on one side and the y’s on the other side like in separable DEs? How do you know when to use this method over separable?

[@iremiposiajayi122]

The question I have is why. Why does mu(x) work? Is there a proof to explain why choosing mu x this way and why following the steps ultimately leads to the product rule?

[@sharifahmed45]

Thanks prof: Sorcerer, you often mention a homework in your lecture in DE playlist, could you please kindly tell me where I can find it?. Thanks for your prompt response.

[@TheMathSorcerer]

Yeah they had online homework for that class, so it was online through a program which is not free. We used something called webassign. I do have practice problems though here on youtube, here is my general playlist on DE kzbin.info/aero/PLO1y6V1SXjjOxAE4cqHXhD2dsO8cnlick If you need specific sections, let me know and I can find the playlists for you. I have playlists for most of the sections. The one I linked above is the "master playlist" which has most of the videos, but I have more. Just let me know:)

[@leonardobranco8829]

I can also use Lagrange's formula, right?

At about minute 18, Why don't we use the multiplication rule for y and x. I think that y is dependent on X. I'd say (1/x)dy/dx - y/(x^2) = sin(x)

[@meetavdoshi4785]

for the very last problem, when you were doing the integration, would taking out 1/sec x be easier than the way you did it (avoiding the simple division of trig functions)? This would result in y=1/sec(x)*(tanx+c), then y=sinx(tanx+c), giving the answer of sinx + c(cosx). I guess it is one more step but the solution remains the same.

[@jackmaes1980]

My professor doesn't explain this as well as you do. When dealing with first order DEs , when should I evaluate using Substitution, and when should I use exact equations. Thank you!!!!!

[@wallybaldemor8523]

Mu or micro?

[@TheMathSorcerer]

Mu

[@TheMathSorcerer]

Oh I see it's micro as an si unit

[@wallybaldemor8523]

1/x quotient rule?

[@morrisonshirmer1742]

Integration factor is not so clear 02:27, listen to Differential Equations Boyce and Di Prima book, 8 th edition, chapter 3, not so explained this, is more complicated and very easy, when correct subject, step by step teacher and not put integration factor as so simple, but not magic formula................... the best choice

[@johndavecusi6990]

Hello sir. Would you solve this equation. I think this is non exact (1-x^2)y'= 1-xy-3x^2+2x^4

[@anjanbhattacharjeesir]

❤

[@SR-kd4wi]

Power series solutions.

[@virusman9452]

Love to Anna 💕