Riccati Differential Equations: Solution Method 

Who would win? A respected Italian mathematician A handsome German boi

Challenge for next video: prove fermats last theorem Easy mode: just solve it Medium mode: use only one piece of chalk Hard mode: do it in under 10 minutes Godmode: impress me

Good morning fellow itallian bois welcome back to a nada video

words cannot describe how grateful I am that your channel exists

The first try was almost good. Riccati (pronounced Rikkati) was offered the same "cathedra" in San Peterburg that Euler accepted.

Italian boi here too 🇮🇹🇮🇹🇮🇹

I've actually been going through my old ODE notes as a refresher and came across the Wronskian. I know how to use it to test linear independence but was never given a proof for why it works. That may be a cool video to add to the series.

Would there also be an elegant transformation in case y, p, q and s are (symmetric) matrices? So when the terms do not necessarily commute.

Good video! Riccati equation is very important in Optimal Control theory.

Hey paps ,what does it mean when Cn coefficients cancel out in 2nd order linear ode while using power series method i.e. you don't get any recursion relation ? ;e.g. something like y'' - y'/x = 0 How to solve it then ?

Man, you make me love DE's again [well, there must be a slightly more adequate way to say that]

Dude that blackboard is just so clean

thanks for the explanation, really helped

Italy here too! Nice video!!

can you explain how you changed t(s’/s + q) into tp(x) at 4:45?

Very interesting ... Thank you very much

is it always morning in your country, Papa Flammy?

Impresionante, felicidades...

Oh my god you are soooo adorable!!! Thank you a lot for the great video!

Hey Pappa Flammy, do you have a favorite textbook on differential equations? I need to learn this subject better.

Excellent work, Greetings from the Middle East ♥️ Iraq ♥️ University of Baghdad

Where are you from teach us ?

Nice - I would like to see some examples

3:56 you're the only qt here

thanks lil bro

Finally! Some real maths

Hahaha, my favorite part was " don't forget your P" nice video!

good efforts

I searched Riccati DE just to find out how is it pronounced and here I get this :DDD

great video boi!

You should finish it ! Is like ripping out the last chapter Of a book and giving it to someone to read

Hey, I am Italian boi

You’re turning me on with all these mathematical physics videos. Given an optimization problem, the second variation guarantees that the extremizer (from first variation, namely the Euler-Lagrange equations) is indeed a local min/max if an associated Riccati equation has a global* solution, i.e. *not* just a saddle point. This is the method of Lagrange, namely patching leaky things until it doesn’t leak anymore. Though I hope your Riccati equation has no solutions daddy because I’d ride your saddle point all night.

First, congratulations for the channel, I am loving it! Second, can you share with me how you make your thumbs? I mean, how you encode Latex with this high quality, like the font is bold, but it isn't. Thank you.

love u ❤️

Flawless

The first guess was about right. Pronounce Riccati as in German “Rickattie” - Stress on the ‘a’. BTW, isn’t this trick also useful in reverse: to convert a 2nd order linear DE into a Riccati equation ? I think I saw something like this somewhere in connection with turning a Schrödinger equation into a Riccati equation? But I might also just all get it completely messed up.

Sweet!!

You should define where the objects are defined. What is the domain of the coefficient function p(x). Most mathematicians who are too rigourous write all details. There is no problem this video is good. But it is not just doing some algebraic computations and getting the answers.

I kn m off subject here but ur accent is 😍😍😍😍

favour this guy\

nice😁

reccati equation x(1-x^2)y'=x^2+y-2xy^2 Please solve this

Oof sexy new channel art, I see u!

You are great, funny, enthusiastic and sexy. I love your performance. Yet, I have a criticism about your approach, although it is quite correct. You transform the Riccati DE in a linear second order ordinary DE (SODE). Correct, but the difficulty remains finding the two independent solutions of this SODE, that is not obvious at all because the coefficients in this SODE depend upon x. This difficulty is equivalent to finding one particular solution for the Riccati equation (notice that once you have a solution of Riccati, you can transform it in a Bernouilli equation, the general solution of which can be easily obtained). By the way, I do research in mathematical physics and I am also interested in teaching like you do. Do you have an advice ? All the best !

Interesting

Boii🔥

Riccati D E = instant like

*good afternoon :)

What engineering did you study?

I only watched this because the lecturer is very attractive 😅😍 But really, it's very very effective when the lecturer is good looking and talks so good.

That's a spicy meatball

Took me some time at first to listen what language he was speaking in and double-check playback speed

At 8:36 shouldn't it be -φ' · P ?

Algerian guys here ❤

heei happiness , flammable are you from german

❤️❤️❤️

Need more clarity in concepts..... Please

int Flammy = funny + math ;)))

i am back! i was busy. who cares?

Papa Jaky at 5:10

I liked the video, but maybe it would be better titled how to transform a Riccati equation into a second order homogeneous ODE (less attractive I know), because this is not a solution. There is no general solution for a second order ODE.

Hold my pee?! Not After going to Octoberfest.

معرفتش نتبع ولا نشوف فيك هههه 😂💕

Ich wünschte, du hättest nen Channel, auf dem du das auf Deutsch machst, dann wäre die Sprachbarriere zu Englisch nicht so groß :/

I can't solve differential equations yet :(

8:58 where is P

🖤

Hi sir... You can solve this problem: find the two different solutions of the diff. Eq. dx/dt=x^2 +p(t)

If one solution is known its easy to reduce it to Bernoulli or linear first order Riccati special can be reduced in some cases to separable If particular solution is not known then we reduce to the linear second order We can also eliminate linear term in Ricatti equation An example of this equation found on forum (x+y)^2 dy/dx - 2y = 0

please y'+y^2=x

It is ItaliAn, not ItaliEn. It is UnpronouncEable, not Unpronounceable. Is is LeviOsa, not LevioSA.

:D

Indian guys here 😎😎

Booooi

I don't like this equation

Im sorry but i think you're talking too fast in my opinion, thats why I barely understand what you're trying to point out in the video

Good day to you I sent you a mail in which i sent you a riccati differential equation that i want you to solve with this method that you discussed but I was told that your email address is not valid and I will very grateful if you can give me your current email address thanks and bye for Now

Sometimes it is useful to do this reduction in reverse (from second order linear to Riccati) Example when reduction to Riccati may help ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-oTDBz9G5yEs.html ---------------------------------------------------------------------------------------------------------------------------------------------------------- If we want back to Riccati I suggest following y''+P(x)y'+Q(x)y=0 y'' = -P(x)y' - Q(x)y | :y y''/y =-P(x) y'/y - Q(x)| -(y'/y) ^2 y''/y - (y')(y')/y^2= -(y'/y) ^2-P(x) y'/y - Q(x) (y''y-(y')(y'))/y^2 = -(y'/y) ^2-P(x) y'/y - Q(x) (y'/y)' = -(y'/y) ^2-P(x) (y'/y) - Q(x) Let y'/y = z then we have z' = -z^2 - P(x)z - Q(x) y'=yz Suppose we have (1+2x^2)y''+6xy'+2y=0 y''+6x/(1+2x^2)y'+2/(1+2x^2)y=0 Riccati equation is z' = -z^2-6x/(1+2x^2)z-2/(1+2x^2) Now particular solution is in the form z_{p}=(ax+b)/(1+2x^2)