Cauchy Euler Differential Equation (equidimensional equation)

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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Update with Lars:
Л.С. Мото
1 hour ago
@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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#differentialequation #math #blackpenredpen

[@aurithrabarua4698]

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

[@blackpenredpen]

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

[@aurithrabarua4698]

All the time 😊😊😊

[@Osama12231]

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

[@aurithrabarua4698]

@@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]

Thank you so much

[@MoonLight-sw6pc]

He wasn't kidding when he said quickly explained .

[@malcom91]

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]

We have wonderful teachers here on yt

[@syahrulmaulanaw6965]

Lmaoo

[@abuabdullaahiwaaaishatah8235]

​@@hconebbortey703 yesssssa

[@lizastewart1976]

Your enthusiasm is amazing and you explained this brilliantly!

[@blackpenredpen]

Thank you!!

[@blackpenredpen]

Why we multiply by ln(x) kzbin.info/www/bejne/aaPZooCrfpyjn8k Be sure to subscribe for more math related videos!

[@Roarshark12]

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]

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]

Have you become the teacher you always wanted to be?

[@SartajKhan-jg3nz]

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

[@diegomullor8605]

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]

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]

@@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]

@@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]

@@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]

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

[@azzizzg8622]

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

[@spelunkerd]

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!

[@santochrome]

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]

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

[@santochrome]

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)

[@icee562]

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

[@jacobs31milkacapuccino]

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

[@protoword10]

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

[@dakotaroberson9921]

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

[@summerflorida5434]

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

[@giovannimariotte4993]

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

[@abuabdullaahiwaaaishatah8235]

New episode of blackpenredpenbluepen my fav 😍😍😍😍

[@abuabdullaahiwaaaishatah8235]

Bprpbp

[@abuabdullaahiwaaaishatah8235]

😍😍😍😍😍😍

[@PunmasterSTP]

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

[@salmaalfawal6155]

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

[@RutvikPhatak]

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

[@lifeispoop8537]

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

[@drpeyam]

LifeIsPoop Thank you!!!

[@sibunabirwasergeon3428]

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

[@silverswordguy4191]

Best channel for DiffEQ. I love you.

[@Macieks300]

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]

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

[@tagekumarpaul7474]

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.

[@Dana__black]

You are my math hero

[@alse72]

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

[@BluePi3142]

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

[@blackpenredpen]

lol!

[@aurithrabarua4698]

best man!!!

[@Gold161803]

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

[@SirBurnsicus]

@@Gold161803 phillip defranco used to say dooblydoo!

[@im.meer-asif]

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

[@phizaics]

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

[@davidsonjoseph8991]

Day after tomorrow*

[@roonilwazlib8137]

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

[@General12th]

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]

It happened! I'm loving it.

[@chemiellee2881]

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

[@andresmanrique8056]

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

[@anthonyjoe9139]

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!

[@Sasquatch4lifeX]

"Just like Spider-the-man"

[@lLl-fl7rv]

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

[@drpeyam]

ODE Deliciousness 😋😋😋

[@Sidou_]

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

[@nikitakipriyanov7260]

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

[@ant0625]

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

[@gordonchan4801]

I like the pace.

[@fredn_]

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

[@nimnim5149]

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

[@joshuakinnard9430]

It's like he wants to die of laughter any second lol 😂

[@MohamedSalah-hp7yy]

Thanks frome Algéria🇩🇿🇩🇿🇩🇿

[@jowillll]

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

[@Xbox360SlimFan]

Dr. Payems German crispy clean. As if there was almost no accent.

[@shubrajchuckowree5670]

This is just so cool🫖

[@shutup3198]

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

[@amirulfadzil7]

Great explanation! Fast and Easy to understand

[@rezamiau]

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

[@vagosplayer]

Im watching in 0.75 speed

[@lightspd714]

Love both channels!

[@ankitpaudel]

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

[@observer4322]

[@artashgyolecyan8498]

Do damped harmonic oscillator equation please🙏

[@giannakiskotsinoxorka1011]

*LOVE YOUR VIDS MAN*

[@youssefjoe521]

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

[@suhailawm]

thank you so much sir

[@razanlb]

that helped me so much thank you !!

[@kairiannah]

thank you teacher

[@mango5660]

very good explanation, thank you :)

[@bizarrelance3698]

Great video thanks!

[@holyshit922]

I prefer change of independent variable x=e^{t}

[@Quadratic4mula]

Since, i, is a constant it is encompassed within, "c2"....

[@safeegull22]

Thanks to you

[@mariokraus6965]

I'm loving/enjoying it :-)

[@jamesudotong]

Awesome!!!

[@stevenstratvert6664]

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

[@Kris-hz1ns]

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 ?

[@cadendennis3019]

I like this guy

[@nothing8752]

Amazing sir 😄😄😄

[@ammar.a2950]

I want to give you a thousand likes

[@dinasamir2778]

Perfect. Thanks

[@ludypalacios2889]

Amazing!!!!!!!!!

[@jzanimates2352]

Get well soon Lars!!!

[@zaranasir5079]

very well explained!

[@ashutoshshivarkar2256]

great video

[@Pedritox0953]

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

[@coincoin8091]

right to the point, I Like it.

[@MengHeangRindali]

I really like your teaching 😍

[@salmael_badry2926]

Yeah, this's so cool!

[@faridahMvungi]

so cool, thanks learn with fun🤣🤣

[@golammartuzahossain6748]

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]

en.wikipedia.org/wiki/Linear_independence

[@Varun73693]

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

[@alefdias4468]

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

[@anubhavshukla4444]

Im happy

[@TechScope2002]

Thanks 😘

[@SmajdalfFrogi12]

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.

[@lambdamax]

If you guys watch this video at 2x speed, you can travel back in time.

[@MoonLight-sw6pc]

so thats pretty much the idea . So i will have to show u guys example to make u guys happy , so I will show u guys example to make u guys happy , lol

[@blackpenredpen]

: ))))

[@mansourativo9658]

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]

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.

[@forthesakeofscience961]

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]

We can.

[@joaofrancisco8864]

SO COOL!!!!

[@CheezPuffz12]

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

[@michaelafful3395]

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

[@holyshit922]

.. and because of case 2 I prefer to change independent variable x=e^{t}

[@13579YOOTUBE]

Very nice

[@chrisstanley9587]

Can anybody help me with this problem? Trying to solve for the complex roots of 9x^3 - 24x + 41 = 0

[@J4M3S247]

Will we be seeing Hermite and Legendre action as well? :D

[@darcash1738]

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