❖ Bernoulli Equation for Differential Equations , Part 1 ❖

[@csandreas1]

i recently received my graade on differential equations and i got 45/45 thanks to Patrick!!

[@MuksEmmaN]

"If you want to see examples of me flying through this stuff". When I grow up I want to have this much confidence :)

[@mar56cos]

I see you have no regards for your own safety by using a permanent marker to do math. = Thug Life!

[@TheUberPeople]

i have a test on this tomorrow, great timing!

[@patrickjmt]

follow up video will available a bit later today

[@jolinchua2011]

me too !! :)

[@elifarley2479]

It's almost exactly a year later, and I am in the same boat. Test tomorrow and this video saves my neck. I wonder if this video's view count will spike 5 weeks into every semester due to the common schedule Diff EQ classes tend to follow.

[@Gataroes]

It's almost 3 months later and I am in the same boat. Test tomorrow and this video saved my neck.

[@supreme_keor]

got a test later, this saves my neck

[@theultimatereductionist7592]

Since learning about the Bernoulli differential equation in the 1980s, I find it's so subtle & amazing & deep why we can solve y'=A(t)*y+B(t)*y^n for any (complex) number n, but not y'=A(t)+B(t)*y^n when n is not 0, 1 or 2 (n=3 is sometimes called the Abel equation).

[@cierramunguia1416]

I'm glad you decided to do a derivation video and a example problems video!

[@Bayonettamachinekill]

It’s incredible how the first program created by Ada Lovelace was all done with Bernoulli equations. Thank you Ada and Charles for inventing the computer.

[@ReWolWerKillZ]

wow i just realised you've never posted this type of D.E. until now. Perfect timing. Differential Equations class just started for everyone in college right now.

[@michaelm6597]

Your videos are amazing and makes this so much more understandable than in class.

[@franpolyphemus4496]

You're a godsend and a lifesaver. Thank you so much for this!

[@coleforbes5443]

Patrick, you have gotten me through calculus. Thanks a lot!

[@TheUberPeople]

You should cover the Ricatti equation too!

[@patrickjmt]

ok, will take a look at it as well

[@Mathemusician97]

I literally just had a test with Bernoulli equations yesterday.

[@steartfires3039]

Brilliant explanation, thanks. That Leibniz was on another level.

[@fredydeekrueger169]

Damn, that sharpie gives me the chills. Great video either way!

[@DehviLz]

This man the reason I passed my class

[@mmmchestnut4085]

odd that I started this really just this week

[@ShInInGReNaGaDe]

Patrick. Thank you.

[@patrickjmt]

+ShInInGReNaGaDe you are very welcome :)

[@alanwrigglesworth7562]

I was wondering if you could do a series on stochastic differential equation. can't find any good videos on it

[@INdoFreakNesian]

great video!

[@robertbrandywine]

Can you use a large whiteboard so that we can see more around what you are doing at one time?

[@kimberlycenbasto7353]

thanks your videos are so helpful 🙂

[@JamesSmith-gq7ru]

Just in time for exams !

[@Docweed13]

Correct me if I am wrong, you are right 98% of the derivation. The problem I see is there should be a negative in front of the a(t) value as the general form is dy/dt + p(t)y = q(t)y^n. Thus your proof would result in dy/dt = - p(t)y + q(t)y^n. Again please advise.

[@MadJDMTurboBoost]

He said suppose you have an equation, y' = a(t)y + f(t)y^n This is an example, and is not derived from the general form equation he had a bit before. It seems confusing but think of it as if the general form is as you wrote it, i.e. dy/dt + p(t)y = q(t)y^n; where a(t) = -p(t), and f(t) = q(t).

[@srinivasanbalan2469]

Hi Patrick, how will I solve the diff equation of the following format. y'(t) = y + f(t) y^n + g(t). Your solution is highly appreciated.

[@fullthrottle254]

THANK YOU PATRICK!!

[@luigiinfanzon2199]

Is that you Patrick?

[@patrickjmt]

i think so

[@luigiinfanzon2199]

I've been watching your videos for a while now but for some odd reason I felt like your voice sounded a bit different on this video, I guess because it's a 2016 video. Nice ring btw, but anyway, I want to take the time to thank you for all the help you have provided all of us throughout the years.

[@rachelilevine1619]

No, its the Crusty Crab

[@jammcrusader1981]

@@luigiinfanzon2199 i agree he def sounds different here haha

[@jammcrusader1981]

​@@luigiinfanzon2199 i thought he sounded different too! but the leftie

[@hari8568]

Patrick I hope u remember a request when i asked if u could possibly analyze few iit mains or advanced papers in maybe ur upcoming videos.a reply would be appreciated.btw this video was very helpful👍

[@yarashamali8061]

i dont get it .. why are the videos in this playlist not in order

[@TheTruthseeker707]

funny as how I started learning this today in class. Is patrickjmt psychic?

[@christiantabalanza4518]

Timing pre-final pa naman sa sabado😘😉

[@jp5568]

FANTASTIC

[@carloschuecos7014]

Patrick, could you tell me how I could solve this diff eq: dy/dx-4xy=4. If I treat it as a linear equation and apply the integrating factor this comes up with the integral of e^(-2x^2) which solution leads me to think that I am doing something wrong. I would appreciate any suggestion from you. Thanks

[@theultimatereductionist7592]

Correct. The final solution is y = exp(2*x^2)*( y(0) +4*integral of exp(-2t^2)*dt from t=x(0) to x). Theorems imply this integral has no elementary solutions in terms of finite compositions of trigonometric functions and exponentials. But, you can always write exp(-2*t^2)= infinite sum of (-2t^2)^n/n! from n=0 to infinity and integrate termwise to get ((-2)^n)*(t^(2n+1))/((2*n+1)*n!) evaluated from t=x upper limit minus t=x(0) lower limit.

[@carloschuecos7014]

Thank you Patric for your answer. You do not know how I appreciate your time giving me your professional solution.

[@narutouchiha1946]

the GOAT

[@harveyarizala7829]

Is that equation z'=(1-n)a(t)z + (1-n)f(t) applicable to any Bernoulli form question?

[@HemAWahEdBas]

I have a test on that tomorrow Wish me luck guys xP

[@sandeepbhuiya29]

All the worst

[@prateeksenapati2152]

Thank you Patrick!!!!!!

[@patrickjmt]

you are very welcome Prateek!

[@fauzansyauqi2815]

Fucking THANKS YOU SO MUCH OMFG DUNNO HOW TO SAY MORE ❤❤❤❤

[@clowheeler]

thank you!

[@patrickjmt]

+carolyn wheeler no problem!

[@chenevan8564]

but if n=0or1 ,how to do it?

[@malkhaz.jokhadze]

Liouville equation next please

[@patrickjmt]

+Malkhaz Jokhadze ok

[@malkhaz.jokhadze]

What about this?

[@abdulwahabmuhammad7668]

هل يوجد مترجم

[@Mohammed_Angler]

great video

[@Misada678]

THANK YOU SO MUUUUUUUUUCH AAAAAAAAAAAAAAA

[@cinbeats2112]

Mat225 sınavına 3 saat kaldı :D

[@carlosaija6851]

very helpful

[@kapallitrijana3168]

great thing i will be very thank full to you

[@TheChanExperiment]

You're amazing

[@AnjaliSharma-bk3vt]

Nice one

[@الحمدللهلاالهإلاالله-ص1و]

Thanks dr

[@makemarshall7041]

Thank you

[@sonaligupta7719]

(xy+e^x)ydx-e^xdy=0 how can we solve this question by bernoulli equation?

[@muhammad_eng]

I have an exam tomorrow ☹️ Pray for me plz💔31/10/2018

[@Madridistooota]

Good luck 💙

[@eunoia6557]

İs he left handed????

[@mevlanisufi2100]

thanks man

[@lysianahwang3969]

holy using a marker for this video was the worst decision cos of that squeaky noise

[@lysianahwang3969]

nevertheless thanks for the video

[@amanbisht9709]

Hmm.. that's what i looking for.

[@erickvillegas8327]

If we use the second equation: y'+a(t)y=f(t) to make the transformation to variables of z, do we get a negative in the front of (1-n)a(t)z in the z' equation? And if so is it significant?

[@zoulikhatebri4859]

Merci

[@madkidjohnny6472]

Odd way of holding the pen.

[@sreeragkr7653]

thanksss

[@james_dinham]

Your video was very instructive, but every time you write that pen is breaking my ears

[@freezinfire]

Cool.

[@souravray7448]

left handed

[@sanzharserik9835]

matan2 )))

[@jolinchua2011]

Thank U !!!

[@qassememad7198]

you are gorgeous