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...
Check out Dr. P and Oreo: • The Oreo Review!
Check out my differential equation playlists for more lessons and tutorials: www.youtube.com/@blackpenredp...
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#differentialequation #math #blackpenredpen

Пікірлер: 225

  • @aurithrabarua4698
    @aurithrabarua46985 жыл бұрын

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

  • @blackpenredpen

    @blackpenredpen

    5 жыл бұрын

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

  • @aurithrabarua4698

    @aurithrabarua4698

    5 жыл бұрын

    All the time 😊😊😊

  • @Osama12231

    @Osama12231

    5 жыл бұрын

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

  • @aurithrabarua4698

    @aurithrabarua4698

    5 жыл бұрын

    @@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

    @Osama12231

    5 жыл бұрын

    Thank you so much

  • @MoonLight-sw6pc
    @MoonLight-sw6pc5 жыл бұрын

    He wasn't kidding when he said quickly explained .

  • @malcom91
    @malcom915 жыл бұрын

    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

    @hconebbortey703

    3 жыл бұрын

    We have wonderful teachers here on yt

  • @syahrulmaulanaw6965

    @syahrulmaulanaw6965

    2 жыл бұрын

    Lmaoo

  • @abuabdullaahiwaaaishatah8235

    @abuabdullaahiwaaaishatah8235

    7 ай бұрын

    ​@@hconebbortey703 yesssssa

  • @blackpenredpen
    @blackpenredpen5 жыл бұрын

    Why we multiply by ln(x) kzread.info/dash/bejne/Zaaq06-ueZrWmco.html Be sure to subscribe for more math related videos!

  • @lizastewart1976
    @lizastewart19765 жыл бұрын

    Your enthusiasm is amazing and you explained this brilliantly!

  • @blackpenredpen

    @blackpenredpen

    5 жыл бұрын

    Thank you!!

  • @Roarshark12
    @Roarshark125 жыл бұрын

    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!!

  • @azzizzg8622
    @azzizzg8622 Жыл бұрын

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

  • @icee562
    @icee5625 жыл бұрын

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

  • @palmoasis
    @palmoasis4 жыл бұрын

    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

    @omaral-absi5478

    2 жыл бұрын

    Have you become the teacher you always wanted to be?

  • @spelunkerd
    @spelunkerd5 жыл бұрын

    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!

  • @PunmasterSTP
    @PunmasterSTP Жыл бұрын

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

  • @SartajKhan-jg3nz
    @SartajKhan-jg3nz5 жыл бұрын

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

  • @roonilwazlib8137
    @roonilwazlib81374 жыл бұрын

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

  • @giovannimariotte4993
    @giovannimariotte49934 жыл бұрын

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

  • @jacobs31milkacapuccino
    @jacobs31milkacapuccino2 ай бұрын

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

  • @dakotaroberson9921
    @dakotaroberson99215 жыл бұрын

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

  • @amirulfadzil7
    @amirulfadzil73 жыл бұрын

    Great explanation! Fast and Easy to understand

  • @lLl-fl7rv
    @lLl-fl7rv3 жыл бұрын

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

  • @RutvikPhatak
    @RutvikPhatak5 жыл бұрын

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

  • @summerflorida5434
    @summerflorida54343 жыл бұрын

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

  • @lightspd714
    @lightspd7142 жыл бұрын

    Love both channels!

  • @giannakiskotsinoxorka1011
    @giannakiskotsinoxorka10115 жыл бұрын

    *LOVE YOUR VIDS MAN*

  • @santochrome
    @santochrome5 жыл бұрын

    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

    @blackpenredpen

    5 жыл бұрын

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

  • @santochrome

    @santochrome

    5 жыл бұрын

    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)

  • @razanlb
    @razanlb Жыл бұрын

    that helped me so much thank you !!

  • @protoword10
    @protoword105 жыл бұрын

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

  • @chemiellee2881
    @chemiellee2881 Жыл бұрын

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

  • @diegomullor8605
    @diegomullor86055 жыл бұрын

    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

    @Super_Smash_Dude

    5 жыл бұрын

    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

    @diegomullor8605

    5 жыл бұрын

    @@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

    @Super_Smash_Dude

    5 жыл бұрын

    @@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

    @diegomullor8605

    5 жыл бұрын

    @@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

    @Super_Smash_Dude

    5 жыл бұрын

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

  • @silverswordguy4191
    @silverswordguy41913 жыл бұрын

    Best channel for DiffEQ. I love you.

  • @abuabdullaahiwaaaishatah8235
    @abuabdullaahiwaaaishatah82357 ай бұрын

    New episode of blackpenredpenbluepen my fav 😍😍😍😍

  • @abuabdullaahiwaaaishatah8235

    @abuabdullaahiwaaaishatah8235

    7 ай бұрын

    Bprpbp

  • @abuabdullaahiwaaaishatah8235

    @abuabdullaahiwaaaishatah8235

    7 ай бұрын

    😍😍😍😍😍😍

  • @mango5660
    @mango56605 жыл бұрын

    very good explanation, thank you :)

  • @nikitakipriyanov7260
    @nikitakipriyanov72604 жыл бұрын

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

  • @bizarrelance3698
    @bizarrelance3698 Жыл бұрын

    Great video thanks!

  • @suhailawm
    @suhailawm2 жыл бұрын

    thank you so much sir

  • @mariokraus6965
    @mariokraus69655 жыл бұрын

    I'm loving/enjoying it :-)

  • @zaranasir5079
    @zaranasir50793 жыл бұрын

    very well explained!

  • @shubrajchuckowree5670
    @shubrajchuckowree56703 ай бұрын

    This is just so cool🫖

  • @ankitpaudel
    @ankitpaudel5 жыл бұрын

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

  • @stevenstratvert6664
    @stevenstratvert66645 жыл бұрын

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

  • @gordonchan4801
    @gordonchan48015 жыл бұрын

    I like the pace.

  • @kairiannah
    @kairiannah3 жыл бұрын

    thank you teacher

  • @lifeispoop8537
    @lifeispoop85375 жыл бұрын

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

  • @drpeyam

    @drpeyam

    5 жыл бұрын

    LifeIsPoop Thank you!!!

  • @andresmanrique8056
    @andresmanrique80564 жыл бұрын

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

  • @jamesudotong
    @jamesudotong3 жыл бұрын

    Awesome!!!

  • @dinasamir2778
    @dinasamir27784 жыл бұрын

    Perfect. Thanks

  • @Dana__black
    @Dana__black3 жыл бұрын

    You are my math hero

  • @safeegull22
    @safeegull223 жыл бұрын

    Thanks to you

  • @ashutoshshivarkar2256
    @ashutoshshivarkar22563 жыл бұрын

    great video

  • @shutup3198
    @shutup31985 жыл бұрын

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

  • @Sasquatch4lifeX
    @Sasquatch4lifeX4 жыл бұрын

    "Just like Spider-the-man"

  • @MengHeangRindali
    @MengHeangRindali5 жыл бұрын

    I really like your teaching 😍

  • @sibunabirwasergeon3428
    @sibunabirwasergeon34287 ай бұрын

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

  • @ludypalacios2889
    @ludypalacios28892 жыл бұрын

    Amazing!!!!!!!!!

  • @alse72
    @alse725 жыл бұрын

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

  • @BluePi3142

    @BluePi3142

    5 жыл бұрын

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

  • @blackpenredpen

    @blackpenredpen

    5 жыл бұрын

    lol!

  • @aurithrabarua4698

    @aurithrabarua4698

    5 жыл бұрын

    best man!!!

  • @Gold161803

    @Gold161803

    5 жыл бұрын

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

  • @SirBurnsicus

    @SirBurnsicus

    4 жыл бұрын

    @@Gold161803 phillip defranco used to say dooblydoo!

  • @nothing8752
    @nothing87522 жыл бұрын

    Amazing sir 😄😄😄

  • @coincoin8091
    @coincoin80913 жыл бұрын

    right to the point, I Like it.

  • @Sidou_
    @Sidou_5 жыл бұрын

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

  • @Pedritox0953
    @Pedritox09535 жыл бұрын

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

  • @salmael_badry2926
    @salmael_badry2926 Жыл бұрын

    Yeah, this's so cool!

  • @salmaalfawal6155
    @salmaalfawal61552 жыл бұрын

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

  • @TechScope2002
    @TechScope2002 Жыл бұрын

    Thanks 😘

  • @joshuakinnard9430
    @joshuakinnard94304 ай бұрын

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

  • @artashgyolecyan8498
    @artashgyolecyan84985 жыл бұрын

    Do damped harmonic oscillator equation please🙏

  • @jzanimates2352
    @jzanimates23525 жыл бұрын

    Get well soon Lars!!!

  • @General12th
    @General12th5 жыл бұрын

    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

    @thedoublehelix5661

    4 жыл бұрын

    It happened! I'm loving it.

  • @joaofrancisco8864
    @joaofrancisco88645 жыл бұрын

    SO COOL!!!!

  • @user-zh6lj2uw6g
    @user-zh6lj2uw6g Жыл бұрын

    so cool, thanks learn with fun🤣🤣

  • @fredn_
    @fredn_3 жыл бұрын

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

  • @anthonyjoe9139
    @anthonyjoe91395 жыл бұрын

    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!

  • @13579YOOTUBE
    @13579YOOTUBE5 жыл бұрын

    Very nice

  • @im.meer-asif
    @im.meer-asif3 жыл бұрын

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

  • @cadendennis3019
    @cadendennis30194 жыл бұрын

    I like this guy

  • @drpeyam
    @drpeyam5 жыл бұрын

    ODE Deliciousness 😋😋😋

  • @MohamedSalah-hp7yy
    @MohamedSalah-hp7yy5 жыл бұрын

    Thanks frome Algéria🇩🇿🇩🇿🇩🇿

  • @jowillll
    @jowillll8 ай бұрын

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

  • @ammar.a2950
    @ammar.a29503 жыл бұрын

    I want to give you a thousand likes

  • @anubhavshukla4444
    @anubhavshukla44445 жыл бұрын

    Im happy

  • @Macieks300
    @Macieks3005 жыл бұрын

    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

    @gregorsamsa9762

    3 жыл бұрын

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

  • @tagekumarpaul7474

    @tagekumarpaul7474

    3 жыл бұрын

    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.

  • @holyshit922
    @holyshit9225 жыл бұрын

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

  • @phizaics
    @phizaics5 жыл бұрын

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

  • @davidsonjoseph8991

    @davidsonjoseph8991

    5 жыл бұрын

    Day after tomorrow*

  • @Quadratic4mula
    @Quadratic4mula5 жыл бұрын

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

  • @youssefjoe521
    @youssefjoe5212 жыл бұрын

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

  • @johanliebert6734
    @johanliebert67345 жыл бұрын

    can you make a vid on biquadratic equations

  • @ant0625
    @ant06252 ай бұрын

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

  • @Kris-hz1ns
    @Kris-hz1ns2 жыл бұрын

    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 ?

  • @Xbox360SlimFan
    @Xbox360SlimFan5 жыл бұрын

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

  • @J4M3S247
    @J4M3S2475 жыл бұрын

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

  • @nimnim5149
    @nimnim51493 жыл бұрын

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

  • @GoonSquadNQ
    @GoonSquadNQ5 жыл бұрын

    Can you use Frobenius method for similar result.

  • @chrisstanley9587
    @chrisstanley95875 жыл бұрын

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

  • @sophonghat9784
    @sophonghat97845 жыл бұрын

    can you do one more of example .

  • @saharhaimyaccov4977
    @saharhaimyaccov49775 жыл бұрын

    7:57 .. how you know all the case (1,2,3)?

  • @forthesakeofscience961
    @forthesakeofscience9615 жыл бұрын

    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

    @himanshnegi832

    5 жыл бұрын

    We can.

  • @SmajdalfFrogi12
    @SmajdalfFrogi125 жыл бұрын

    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.

  • @CheezPuffz12
    @CheezPuffz125 жыл бұрын

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

  • @adeos5442
    @adeos54423 жыл бұрын

    Love u

  • @observer4322
    @observer43222 жыл бұрын

  • @faridjeb
    @faridjeb5 жыл бұрын

    hello dear prof, if you can help me, i search a solution for this : y'+a y^2 = b

  • @varlandan5245
    @varlandan52455 жыл бұрын

    Can someone find x if he is equal to (2+1)*(2^2-1)*(2^3+1)*(2^4-1)......*(2^2019+1) ?

  • @davidramos4707
    @davidramos47072 жыл бұрын

    What’s the real difference between observe and note?

  • @rezamiau
    @rezamiau5 жыл бұрын

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