Cauchy Euler Differential Equation (equidimensional equation)

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I will introduce the Cauchy-Euler differential equations, aka the equidimensional equation, nonlinear second order differential equation ax^2y''+bxy'+cy=0,
Reduction of order, why we multiply by ln(x), • solving 4x^2y''+y=0 by...
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@blackpenredpen Thank you. I was released today early morning (almost 5pm in Europe now), and I feel so much better currently than after my first heavy session. I'm actually constantly hungry, and can't stop eating, and don't feel tired at all. No throwing up, no other symptoms at the moment... I feel absolutely great... hope it stays this way :)
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Here's the Euler's Formula: • Euler's Formula (but i...
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Опубликовано:

15 окт 2024

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Комментарии : 226

@aurithrabarua4698 5 лет назад

Loved the collaboration of bprp and Dr. Peyam wishing recovery of Lars 😊😊😊 Not just only integrating equations but most importantly integrating humanity

@blackpenredpen 5 лет назад

Thank you!!! He is a mutual viewer of ours! We wish him and everyone the best!

@aurithrabarua4698 5 лет назад

All the time 😊😊😊

@Osama12231 5 лет назад

The integral of sin2x cos2x without using the (U) way

@aurithrabarua4698 5 лет назад

@@Osama12231 Easy man, bring on a 2, but in the same way we have to divide by two or multiply by 1/2, then it will represent a formula of sin2x=2 sinx cosx, so the expression will be sin4x and a half as a mutiple. Just because 1/2 is a constant term, bringing forth of the integral sign, we will integrate. the answer will be -1/8 cos4x

@Osama12231 5 лет назад

Thank you so much

@MoonLight-sw6pc 5 лет назад

He wasn't kidding when he said quickly explained .

@malcom91 5 лет назад

Did I just learned in 13 minutes something my calculus teacher wasn't able to teach us in a comprehensive manner during one month of class? You're a BRILLIANT teacher. I had to say it

@hconebbortey703 3 года назад

We have wonderful teachers here on yt

@syahrulmaulanaw6965 3 года назад

Lmaoo

@abuabdullaahiwaaaishatah8235 10 месяцев назад

@@hconebbortey703 yesssssa

@lizastewart1976 5 лет назад

Your enthusiasm is amazing and you explained this brilliantly!

@blackpenredpen 5 лет назад

Thank you!!

@blackpenredpen 5 лет назад

Why we multiply by ln(x) ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-3rvqMuI7pig.html Be sure to subscribe for more math related videos!

@Roarshark12 5 лет назад

Steve and Dr. Payam, I LOVE your enthusiasm--I found myself nodding when I learned something new and smiling at how many areas of math the solution touched on :-) Thanks so much!!

@palmoasis 5 лет назад

I am so grateful for the efforts you put in your explanations, i aspire to become such a great teacher as you clearly are, keep up the great videos you're making and Thanks a million!

@omaral-absi5478 2 года назад

Have you become the teacher you always wanted to be?

@spelunkerd 5 лет назад

I like this fast presentation method for video learning. The pause and replay buttons get used a lot, but there's nothing wrong with that!

@azzizzg8622 Год назад

I love your videos so much. Thank you a billion times. You are saving my semester!!!

@santochrome 5 лет назад

I found this channel from the 100 integrals video and I have to admit, I watched ALL of it and im STILL watching.. I dont think i ever realised how much I like maths lol

@blackpenredpen 5 лет назад

Wow, amazing! : )))) I am very glad to hear, thank you!

@santochrome 5 лет назад

blackpenredpen i think i am going to show my further maths class the last integral you did and see if they spot how to do it.. (you know, the VERY last integral :D)

@SartajKhan-jg3nz 5 лет назад

Never speedrun such differential eqns ever again. Everything went over my head...but that complex part was 🔥🔥

@icee562 5 лет назад

Thanks a lot for deriving the general solution for complex roots. Fantastic!!!

@diegomullor8605 5 лет назад

Cool! I absolutely love your videos man! Thanks for making a 14 (almost) year old like me discover his passion for calculus and learning about integrals and derivatives! Thanks a lot man, I really mean it. Keep it up. Edit: Also I forgot to say: Good luck in your recovery Lars!

@Super_Smash_Dude 5 лет назад

You're almost 14 years old and watching videos on calculus...and enjoying it!!!?? That's pretty awesomeXD I didn't get to calculus until I was 18! I love maths, so it's a pleasure to meet math lovers like you:)

@diegomullor8605 5 лет назад

@@Super_Smash_Dude That's the beauty and magic of the internet when used right. Who says you've got to wait years bored in class? If you're good at something, use the internet to get better. I'm really thankful to have the internet.

@Super_Smash_Dude 5 лет назад

@@diegomullor8605 So true my friend:) I learnt a huge amount of math from the internet. I'm really grateful the internet exist(despite some of the bad stuff).

@diegomullor8605 5 лет назад

@@Super_Smash_Dude Yeah. If it wasn't for the internet I wouldn't even speak English properly. YT Channels with communities like blackpenredpen's make you realize that our "new" generation isn't "wrong" or have no interest. People do still appreciate math and other things. Thanks for making my day a bit better!

@Super_Smash_Dude 5 лет назад

@@diegomullor8605 I honestly wish there we're more people like you. You've actually made my day!

@giovannimariotte4993 4 года назад

You are not aware of how much has this video helped me

@summerflorida5434 3 года назад

You used different variables than my professor. But explained it 10x better. Thank you!

@alse72 5 лет назад

So this section is now called the "denominator", huh

@BluePi3142 5 лет назад

I mean, YTers do ask viewers to comment down below...

@blackpenredpen 5 лет назад

lol!

@aurithrabarua4698 5 лет назад

best man!!!

@Gold161803 5 лет назад

Add it to the list: the sidebar, the dooblydoo, my pants, the towel section, the denominator...

@SirBurnsicus 4 года назад

@@Gold161803 phillip defranco used to say dooblydoo!

@dakotaroberson9921 5 лет назад

gute Besserung, und ich weiß, dass du bald sehr glücklich sein wirst!

@im.meer-asif 3 года назад

what is the solution of Y"-kY=0 defined on 0

@protoword10 5 лет назад

As you have Euler, you have also Bernoulli, than Rickety, than etc...It’s nice to remember those college days...Thank you!

@abuabdullaahiwaaaishatah8235 10 месяцев назад

New episode of blackpenredpenbluepen my fav 😍😍😍😍

@abuabdullaahiwaaaishatah8235 10 месяцев назад

Bprpbp

@abuabdullaahiwaaaishatah8235 10 месяцев назад

😍😍😍😍😍😍

@PunmasterSTP Год назад

Thanks so much for the explanation and examples! The Euler differential equation was something I was really trying to come to terms with.

@silverswordguy4191 3 года назад

Best channel for DiffEQ. I love you.

@sibunabirwasergeon3428 10 месяцев назад

Doctor you are really a good teacher. May the Almighty GOD bless you

@roonilwazlib8137 4 года назад

I really like your enthusiasm and love for mathematics!! good video

@gordonchan4801 5 лет назад

I like the pace.

@jacobs31milkacapuccino 5 месяцев назад

Thank you at thousand times from my soul(от души)☺☺☺

@salmaalfawal6155 2 года назад

My exam is literally tomorrow and you saved me after crying for 15 mins

@chemiellee2881 Год назад

This is so cool my man I miss class but yeah you got me! thanks so much

@Macieks300 5 лет назад

I got everything but you didn't convince me that there aren't any different solutions. You just assumed in the begining that y=x^r but what if it's not the case.

@gregorsamsa9762 3 года назад

Welcome to differential equations, all that work is done by smart people with proofs we can't understand

@tagekumarpaul7474 3 года назад

in the observations he said that the solution needs to be focused around powers. Simply put, the solution for these types of equations have to be something that differentiates into a similar value (not too different). Thus when you plug it back in, it will give you the original equation. Also he proved that after.

@lifeispoop8537 5 лет назад

Oh wow, I thought I was on the wrong channel. I love ur Gaussian Integral series

@drpeyam 5 лет назад

LifeIsPoop Thank you!!!

@jowillll 10 месяцев назад

Love the explanation! However, is there a video explaining 6:50? I'm confused on why he used lnx above other functions

@anthonyjoe9139 5 лет назад

I'm just kind of amused that every time you step off screen with your dark track suit the camera auto dims. When you step back on screen the brightness then increases. When you're on screen it's brighter!

@phizaics 5 лет назад

Day after tomorrow is senior secondary mathematics examination of 12th standard students in India. Wish us luck. Thank you.

@davidsonjoseph8991 5 лет назад

Day after tomorrow*

@General12th 5 лет назад

I hope 3Blue1Brown does a series on differential equations some day. I've followed some online resources, but he really knows how to make the ideas click!

@thedoublehelix5661 5 лет назад

It happened! I'm loving it.

@RutvikPhatak 5 лет назад

Bprp I always love your videos! They're through and well explained! I wish you were my teacher! Your students are lucky!

@lLl-fl7rv 4 года назад

This dude is a beast. Thanks for the explanation!!!

@amirulfadzil7 4 года назад

Great explanation! Fast and Easy to understand

@Sidou_ 5 лет назад

Please we need the integral of [sqrt(x)*cos(x)]

@andresmanrique8056 4 года назад

My midterm is in 2 days you're saving me right now :)

@lightspd714 2 года назад

Love both channels!

@ankitpaudel 5 лет назад

i have learnt a lot of math concepts from your videos so please make a series of higher order differential equation.

@Dana__black 3 года назад

You are my math hero

@Sasquatch4lifeX 5 лет назад

"Just like Spider-the-man"

@rezamiau 5 лет назад

Please ,Please and Please SLOW DOWN!!!!! you're a very good tutor and you don't need to be fast !!

@Kris-hz1ns 2 года назад

Hello @blackpenredpen, you say at 7:10 to use x^r1*ln(x) as the other independent solution if r1=r2. However, when I tried with the diff. eqn. you formed with y=x^4 as the solution in the beginning, i.e., x^2y'' + xy' - 16y = 0, x^4*ln(x) does not satisfy this differential equation... did I misunderstand you ? Could you please explain ?

@drpeyam 5 лет назад

ODE Deliciousness 😋😋😋

@shutup3198 5 лет назад

I had trouble understanding the accent but its still very well explained and it helped me a lot

@nikitakipriyanov7260 4 года назад

Niiice. I correctly guessed your example before you reveal it on the board :)

@darcash1738 6 месяцев назад

does it work 4 anything non-power func? if so, whats that called

@giannakiskotsinoxorka1011 5 лет назад

*LOVE YOUR VIDS MAN*

@mansourativo9658 8 месяцев назад

What if the root is 0? Does that mean when you substitute 0 to x^m, we get C1x^0 or just equal to C1? Or is there another case for root that is equal to 0?

@realcirno1750 8 месяцев назад

yeah if 0 is a root then theres a constant term in the general solution. You can actually see this by inspection since the ODE will only have a y'' and y' term and no y so the homogeneous ODE must have a constant solution.

@fredn_ 4 года назад

i cant express how much i love you, you must be protected at all times calculus god almighty

@artashgyolecyan8498 5 лет назад

Do damped harmonic oscillator equation please🙏

@razanlb Год назад

that helped me so much thank you !!

@shubrajchuckowree5670 6 месяцев назад

This is just so cool🫖

@CheezPuffz12 5 лет назад

Is there a video that shows this when the differential equation is not equal to 0

@shayannazeer8104 4 года назад

hey @blackpenredpen why are you using blue pen?

@SmajdalfFrogi12 5 лет назад

Why exactly do you in the third case take the sin and cosive as the solution? It seems to me that it should only be two cosine functions, after you plug in the +- beta part.

@golammartuzahossain6748 5 лет назад

Can you please explain these terms linearly dependant and linearly independent in a video? I still don’t get it.You have even used the terms while talking about case 2

@Macieks300 5 лет назад

en.wikipedia.org/wiki/Linear_independence

@Varun73693 5 лет назад

He has made a lot of videos on this. Look it up.

@alefdias4468 5 лет назад

Well, there is a definition for the inner product of two functions, if it works out to be zero they are linearly independent, it's a really useful concept in proving the Fourier series for example. There is also a complex analysis theorem to justify the complex part of the solution as a solution to the ODE equation being a solution, if I remember well the function has to be analytical

@michaelafful3395 2 месяца назад

PLS CAN U SHOW ME IF THE POWER OF X IS 3 OR THIRD ORDER THANKS

@youssefjoe521 2 года назад

to solve the ODE you need to change the variable by putting Z(t)=Y(exp(t))

@stevenstratvert6664 5 лет назад

Awesome. I'm going to use this in making sound waves

@skc4188 Год назад

Can this be solved by using Frobenius series as well?

@jzanimates2352 5 лет назад

Get well soon Lars!!!

@davidramos4707 3 года назад

What’s the real difference between observe and note?

@forthesakeofscience961 5 лет назад

Hey can u answer my one question why can't we apply differentiation under integral sign on simple integrals too?? And if we can then can u plz make a video on how can we???

@himanshnegi832 5 лет назад

We can.

@ThePharphis 5 лет назад

Did you explain the ln(x) factor being necessary for linear independence in another video? Just catching up on some old ones so I'm not sure

@edgarcalochcampos1930 5 лет назад

check the description

@ThePharphis 5 лет назад

thanks!

@Pedritox0953 5 лет назад

Great video! Please next video plot the function and maybe variate the values

@mango5660 5 лет назад

very good explanation, thank you :)

@suhailawm 2 года назад

thank you so much sir

@MohamedSalah-hp7yy 5 лет назад

Thanks frome Algéria🇩🇿🇩🇿🇩🇿

@nimnim5149 3 года назад

what he is having doraemon soundtrack in the background....... well this trick worked ... it definitely increased my interest in the video .... lol

@ant0625 4 месяца назад

thumbnail let us know he was Asian and he had glasses and it lived up to that standard, thanks man

@volodyanarchist 5 лет назад

I'm sorry, i am completely lost, how you can just drop the imaginary part?

@Yellowgary 5 лет назад

Someone can correct me if I’m wrong but I believe it’s because usually you would have a constant before your function so you would be able to merge the constant with i to create a new constant and label it something else. For example Cisinx=Ksinx so you practically forget about the imaginary part

@volodyanarchist 5 лет назад

@@Yellowgary OK, so we have a function in the form A+Bi. Let's say you add a constant before that function, you would need to distribute it amongst both parts of the sum. I am not purposefully trying to be stupid here, i honestly do not see this.

@kairiannah 3 года назад

thank you teacher

@limitstates 2 года назад

Great video thanks!

@zaranasir5079 3 года назад

very well explained!

@hugocoolens 5 лет назад

Is there a reason why the autocaptions can't be enabled for this clip? There is no CC (closed captions) icon to the left of the cog wheel. These auto captions are really a great help for me.

@marcushendriksen8415 5 лет назад

Auto captions can't get words right even under normal circumstances; the chances of it working properly to translate words to maths are minuscule

@hugocoolens 5 лет назад

I don't agree. Depending on the speaker it can work remarkably well. For blackpenredpen it normally works really good. This is the first clip for which I can't activate it. Something must have changed...?