Cauchy Euler Differential Equation (equidimensional equation)
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- Опубликовано: 15 мар 2019
- 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
Loved the collaboration of bprp and Dr. Peyam wishing recovery of Lars 😊😊😊
Not just only integrating equations but most importantly integrating humanity
Thank you!!! He is a mutual viewer of ours! We wish him and everyone the best!
All the time 😊😊😊
The integral of sin2x cos2x without using the (U) way
@@pyromancer1127
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
Thank you so much
He wasn't kidding when he said quickly explained .
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
We have wonderful teachers here on yt
Lmaoo
@@hconebbortey703 yesssssa
Your enthusiasm is amazing and you explained this brilliantly!
Thank you!!
Why we multiply by ln(x) ruclips.net/video/3rvqMuI7pig/видео.html
Be sure to subscribe for more math related videos!
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!!
I love your videos so much. Thank you a billion times. You are saving my semester!!!
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!
Have you become the teacher you always wanted to be?
Thanks a lot for deriving the general solution for complex roots. Fantastic!!!
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!
I really like your enthusiasm and love for mathematics!! good video
Thanks so much for the explanation and examples! The Euler differential equation was something I was really trying to come to terms with.
*LOVE YOUR VIDS MAN*
Never speedrun such differential eqns ever again. Everything went over my head...but that complex part was 🔥🔥
Love both channels!
This dude is a beast. Thanks for the explanation!!!
Bprp I always love your videos! They're through and well explained! I wish you were my teacher! Your students are lucky!
gute Besserung, und ich weiß, dass du bald sehr glücklich sein wirst!
Thank you at thousand times from my soul(от души)☺☺☺
You are not aware of how much has this video helped me
Great explanation! Fast and Easy to understand
that helped me so much thank you !!
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!
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:)
@@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.
@@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).
@@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!
@@diegomullor8605 I honestly wish there we're more people like you.
You've actually made my day!
You used different variables than my professor. But explained it 10x better. Thank you!
Best channel for DiffEQ.
I love you.
very good explanation, thank you :)
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
Wow, amazing! : )))) I am very glad to hear, thank you!
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)
Great video thanks!
very well explained!
I'm loving/enjoying it :-)
This is so cool my man I miss class but yeah you got me! thanks so much
thank you so much sir
As you have Euler, you have also Bernoulli, than Rickety, than etc...It’s nice to remember those college days...Thank you!
Perfect. Thanks
Niiice. I correctly guessed your example before you reveal it on the board :)
New episode of blackpenredpenbluepen my fav 😍😍😍😍
Bprpbp
😍😍😍😍😍😍
Oh wow, I thought I was on the wrong channel. I love ur Gaussian Integral series
LifeIsPoop Thank you!!!
Awesome!!!
i have learnt a lot of math concepts from your videos so please make a series of higher order differential equation.
thank you teacher
This is just so cool🫖
Thanks to you
great video
Amazing!!!!!!!!!
I like the pace.
Awesome. I'm going to use this in making sound waves
Amazing sir 😄😄😄
My midterm is in 2 days you're saving me right now :)
You are my math hero
right to the point, I Like it.
I really like your teaching 😍
SO COOL!!!!
Yeah, this's so cool!
Great video! Please next video plot the function and maybe variate the values
Thanks 😘
I had trouble understanding the accent but its still very well explained and it helped me a lot
Very nice
So this section is now called the "denominator", huh
I mean, YTers do ask viewers to comment down below...
lol!
best man!!!
Add it to the list: the sidebar, the dooblydoo, my pants, the towel section, the denominator...
@@Gold161803 phillip defranco used to say dooblydoo!
Get well soon Lars!!!
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!
Do damped harmonic oscillator equation please🙏
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!
It happened! I'm loving it.
Will we be seeing Hermite and Legendre action as well? :D
My exam is literally tomorrow and you saved me after crying for 15 mins
Love the explanation! However, is there a video explaining 6:50? I'm confused on why he used lnx above other functions
I like this guy
Please we need the integral of [sqrt(x)*cos(x)]
Doctor you are really a good teacher. May the Almighty GOD bless you
"Just like Spider-the-man"
It's like he wants to die of laughter any second lol 😂
so cool, thanks learn with fun🤣🤣
Im happy
i cant express how much i love you, you must be protected at all times calculus god almighty
I want to give you a thousand likes
Thanks frome Algéria🇩🇿🇩🇿🇩🇿
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 ?
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.
what is the solution of Y"-kY=0 defined on 0
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.
Welcome to differential equations, all that work is done by smart people with proofs we can't understand
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.
ODE Deliciousness 😋😋😋
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.
Auto captions can't get words right even under normal circumstances; the chances of it working properly to translate words to maths are minuscule
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...?
to solve the ODE you need to change the variable by putting Z(t)=Y(exp(t))
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???
We can.
Day after tomorrow is senior secondary mathematics examination of 12th standard students in India. Wish us luck. Thank you.
Day after tomorrow*
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
check the description
thanks!
Who is Lars?
can you make a vid on biquadratic equations
thumbnail let us know he was Asian and he had glasses and it lived up to that standard, thanks man
Love u
Can this be solved by using Frobenius series as well?
Im watching in 0.75 speed
Is there a video that shows this when the differential equation is not equal to 0
hey @blackpenredpen why are you using blue pen?
.. and because of case 2 I prefer to change independent variable x=e^{t}
Can you use Frobenius method for similar result.
does it work 4 anything non-power func? if so, whats that called
7:57 .. how you know all the case (1,2,3)?
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
en.wikipedia.org/wiki/Linear_independence
He has made a lot of videos on this. Look it up.
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
Since, i, is a constant it is encompassed within, "c2"....