Substitutions for Homogeneous First Order Differential Equations (Differential Equations 20)

[@emmett1]

Professor Leonard needs a Netflix original series

[@ayeshaali3990]

yesssss

[@BrandonLindquist]

I think he's in the first season of Altered Carbon (Joel Kinnaman)

[@obayrafi2632]

No matter how much i search for it You are the only teacher i can understand calculus to Even tho im not a native english

[@Peter_1986]

One great thing about Professor Leonard is that he always gives several straightforward example problems fairly early. Most of my math teachers have stood and rambled on forever about proofs and theorems and confusing crap, and then they MIGHT have given one example problem - and it was always a very long, tedious problem, every single goddamn time.

[@parinpatel5719]

Though I understand your pain, you should also be thanking your teachers. Many students dislike math because they don't know why they're doing it or where it comes from. Many teachers only give several examples and call it a day. When learning math, it's always important to know the derviation of the formulas you learn, and why certain concepts are the way they are. Any college student here would perhaps agree on this.

[@pedrosantana3283]

@@parinpatel5719 That's only useful when we can understand the proofs, and even then they're only really good for math majors. Professor leonard makes it clear what to do with it as a tool, and that's what engineers see math as.

[@thomasjefferson6225]

@@pedrosantana3283 Leonard shows the derivation through his lectures. He spent an entire video explaining what exact solutions are and how they're derviaived. So I think hes a perfect blend of teaching theory and giving examples. Blessed we are to have this resource. I cannot find anything of this quality for real analysis or theoretical optimization. Im scared to attack abstract algebra and topology, since there isnt a professor leonard for those subjects... honestly.

[@hamzakharmaz6627]

he is literally teaching me and give me motivation after the video to go gym. who needs more than that?

[@Nic-of1sr]

The main thing I got from this video "When you get angry at your math, it's ok. Walk away, take a break and come back to it later." I felt this.

[@sohaibabbasi3355]

Same but I never come back

[@nick_hf]

[ASMR] Swole smart math boyfriend puts you to sleep while giving you a lecture about Homogeneous First Order Differential Equations.

[@isabellouise8164]

hahahahahahahahahahah :'D

[@geezeeelgee]

BHAHABAHAHHA PLZ-

[@roeal-wazeer3135]

LMFAOOOO

[@Spooly_]

Man this is so much simpler and more understandable than the way I was taught in class. I went from tearing my hair out, to solving these problems rather quickly. Thanks Leonard. ps As an extra benefit I find myself not just more motivated to do math but also to hit the gym, I wonder why that is.

[@wilsonnarea5378]

Gym lectures

[@zaeemattique7086]

Yep, I'm still waiting for this guy to drop his training routine

[@NeverendingAbyss]

Thank you for warning us about anger! This is the first math class that I really was infuriated by it. I'll take your advice and take a break when I feel angry. :)

[@vaughnmonkey]

ya I'm glad he said it too because my professor for this course seems to enjoy us getting frustrated and angry. He actively pursues it and without Professor Leonard I would have given up on this class by now.

[@amjad6361]

You deserve to pause my AdBlocker for you, you are a great man!

[@elijahachiekpanchol2772]

your teaching approach is so unique and wonderful. the last time I check no mathematics teacher would make this topic as easier has you have made it. I am so grateful professor keep doing this Good work for the world.

[@ccutler4159]

At 36:55 I did the same technique but using property of square roots then exponents. Right away, I noticed \sqrt{xy}=\sqrt{x}\sqrt{y} since it was all over x I then used the property of exponents to simplify. Super cool to see how different brains process and think when working through problems. I am almost done with my BS in Pure math just going back to previous classes to not lose the skills. Thank you so much!

[@KK-od2vy]

I can't thank you enough for explaining things step by step. I wish all teachers were like you!

[@eipiplusone3791]

Then all the gyms in the world would be constantly crowded.

[@KK-od2vy]

eipi plusone lol you what I mean. I am talking about his teaching strategies here.

[@shadydesu]

the gains on this math lad

[@jennifermobley1440]

I think every professor should tell their students your speech about getting angry. I have noticed time and time again when I get angry, I am no longer taking in any information. I have to walk away!!! Thank you for always being so awesome Professor Leonard. I wish you'd come back and make more videos. I really could have used your help with Eulers method and then the improved Eulers method!

[@j.o.s.h.o]

dont even attend lectures in uni for diff. eqs. just watch these videos. Thank you so much for them!

[@douggwyn9656]

Thanks especially for the final segment concerning domain restrictions. It's not just nit-picking; over the years I've seen many practical cases where lack of attention to this detail have produced incorrect or incomplete results.

[@ProfessorLeonard]

Absolutely, and I'm glad you enjoyed it. Lately, I've been of the mind to get the technique understood first and then, once that's mastered, to explain the finer points of what's really going on "behind the scenes" so to speak. Students seem to grasp the domain restrictions better once they have mastered what they are actually doing and why the are doing it. Thanks for watching!

[@douggwyn9656]

Your approach does seem like the most effective plan. Even a quick mention early on that there are details to be examined later is enough to damp down a tendency to ignore them. Thanks again!

[@3426-y2t]

i spent hours trying to understand the book but you made it better

[@julietgenshin5193]

Thank you always professor, always love the pep talks too ❤️❤️

[@mikehughes6582]

I'll bet his classes fill quickly. He's the best I've seen.

[@oneofyk]

Thank you professor. This lesson helped a lot.

[@rababalnajjar3170]

Finally I understood. Thank you so much professor Leonard :)

[@mariamsal8531]

Sir ...God bless you and keep you, may He make his face shine upon you and your family.

[@jessieshepard7789]

come teach at CSU PLEASE!!! my professor is so hard to follow that I watch your videos during class time rather than go to class and I gain SOOO much more comprehension. THANKYOU!!!

[@SakeKaama]

You're a wonderful online lecturer, which is hard to do. Thanks for teaching me DE Professor Leonard

[@bunkydunk7500]

Wow this was so clear and helpful! I am very grateful for this excellent video!!!!

[@jstadler417]

Thanks for another great lecture, Professor Leonard!

[@lorenzomenegol6461]

Jesus christ, those mathematical arms 😍

[@user-rj7cq1cy8b]

😂😂

[@geezeeelgee]

i laughed way too hard at this

[@sohaibabbasi3355]

Looool

[@mishaivanov205]

love this guy so much. I always feel dumb in my math lectures because all these professors have nothing on leonard... This is what education looks like^^

[@faismasterx]

These examples are so neat and tidy compared to the monsters we used to get on exams.

[@lindseytreweek8771]

Your reminder to not get angry about math (around minute 15) came at a perfect time!! :) Thank you!

[@bossrollup6920]

This channel may have saved me this semester, also why is no one commenting on how absolutely YOKED this man is?

[@danialdunson]

Leonard looking jacked. Never thought i'd still be watching you after 4 years of college

[@johnholme783]

Elegant solution! So simple yet so useful! Thank you!

[@rorymackinnon6133]

We need more people like you

[@jeffreymoses7131]

This guy was sent from the heavens

[@rudnam]

44:34 wow just when i was wondering if i skipped something or was at the wrong video a problem very similar to the one on my hw shows up lol, you're a god

[@Salamanca-joro]

14:17 i have this problem with programming , thanks for the advice

[@Lestibournes]

You can have a square root of 0 (which gives you 0). The only problem is with a square root of a negative number. Therefor you do need both x != 0 and xy >= 0.

[@MartialJus]

Wow Just simplified this problem for me... Never understood this in class 😊

[@robert_redd1528]

professor leonard is a total mmath guru

[@anirudhkundu722]

when i listen to it in class, i think im the fish out of the sea. Here after watching i think i know kungfu

[@michaeljjan6344]

For 1:05:08, you talk about domain. When you say x*y>0, why can't y=0?????

[@Exoudar]

Hey professor, First, I would like to thank you for teaching us. Second, I have only one problem with this method (I know I am the problem, not you). For example, the following problem is really difficult to solve using the method I learned from you. Or maybe I am doing something wrong? But when I searched for a solution, all the solutions I have found are using different methods for the specific problem I am facing. x dx + (y -2x) dy = 0 Would love to be able to solve it using the method I learned from you.

[@meesumali4278]

I got you , you are superman no more hiding clark

[@flyingvelociraptor2]

Every video, this man keeps getting buffer. Soon he will be the hulk

[@vaughnmonkey]

I don't understand how you can do that x into the square root of x^2? why is that allowed?

[@mesh97__]

man .. you are the best proff I ever seen :} for real..

[@Ssm19494]

feels good when you can do example 2 in 15 seconds and 8 lines of math

[@johnorangez2508]

To my book this is art not math ! Thanks professor!!!

[@elevated__arts]

Do you work out, Professor?

[@jayrocapela]

*brofessor

[@ElNietoPR]

Dominik B nah, he got that body by finding limits.

[@Jay_GTR]

El Nieto PR lmao 😂

[@ayeshaali3990]

@@ElNietoPR lol

[@lanimulrepus]

Blast from the past! 😎

[@oak6677]

the way he points those 'little' details(like (x^2)^0.5 makes me really think deeply about math....thank you Professor!

[@p27kushagra]

I like it when Henry Cavill is teaching me.

[@ClabClab]

you are a godsend.

[@theinquiringengineer]

This dude looking like a smart Jonny Bravo

[@schloshyjea1]

Oh my gosh. Spot on.

[@faismasterx]

Johnny Bravo's smarter younger brother.

[@maldova]

Those biceps are out of this world

[@Khronos_Aion]

@ 17:10 when he says "is it linear ----- NO... kills me every single time

[@wqewqe1350]

You saved my marks❤️❤️

[@VectorSpace33]

PLEASE HELP ME UNDERSTAND. Why is his definition of Homogenous D.E. different than everyone else's. That definition being f(tx,ty) = f(x,y).

[@CurryMuncher2]

I belive both definitions are equivalent

[@nazifataha8868]

Nothing compares to your ways of teaching love it!

[@markzho]

Thank you for showing all the steps! I greatly appreciate it.

[@lorenapadilla1912]

I love him

[@Jessica-hl4mo]

You’re the best!

[@isaakdaniel1422]

At 53:00 Im a little confused with that split professor. Isn’t it ilegal to separate it since there’s more than one term in the denominator?

[@walijamali9476]

I am confused. My teacher told me when I was doing the question x-y/x+y that the numerator and denominator have the same power, hence it's a homogeneous equation. Can anyone plz tell me if this approach is correct?

[@CurryMuncher2]

I would divide numerator and denominator by x

[@j.o.s.h.o]

At 55:00 would it be wrong if you accidentally left the absolute value lines? Don't think it would really affect things, but can anyone confirm?

[@hrithicksen3644]

Man, what pen do you use? I wanna get bulky arms too 😯

[@jheybrent]

Why does the derivative of y=vx is dy=vdx+xdv in our book(dx is included). Tried solving the first problem with same approach on our book but i cant get it. Welp

[@pedrolotti45]

thanks from Brasil

[@jevcampbell2301]

I swear You are the best... You and PatrickJMT are the only reason I see a light at the end of this tunnel...

[@oak6677]

1:03:43 but y could be zero so shouldn't we have the restrictions xy>0 n xy=0 n x not equal to 0 ?

[@wildchild1161]

When we are creating the y/x substitution don't we have the potential to be dividing by zero ? If how do we handle it ? just say x cannot = 0 ?

[@seemasood3840]

sir please discuss linear programming in your future video lectures and also linear regression.

[@rainbowburritoguy]

Hello Professor Leonard, I know I'm late to the party, but I was wondering why you didn't completely solve for y (left it as y^2) during the first homogeneous example (somewhere around 33:00). If anyone wants to tune in and provide an explanation it would be greatly appreciated.

[@f-22raptor25]

square root would make it + and -; we dont know if its positive or negative. Leaving it as y^2 is better when you have no values. He also kinda explains it 32:28

[@LittleJoyous]

It's implicit

[@garyge3204]

Man if my math professor is buff like him id prolly get A for all my midterms.

[@Mohd_ao]

شكرا لك

[@kvnagendra5354]

*127 likes without a single dislike...... U deserve it*

[@mimihoeller9213]

for the second example problem, can you use a substitution v = y-x?

[@monkeydrums1]

Best explanation out there, absolute life saver

[@DittyWolf]

What are you supposed to do if you get dv +v? How do you solve this.

[@theoendre6484]

Superb lecture!

[@saisanjithkakkireni2041]

Thank You

[@mickwellhamakoma4854]

professor it was awesome.

[@himnishchopra6204]

thank you for the video sir

[@hilariousharry1890]

professor would be great if you please start a trig series too!

[@sorrello6328]

good help here!

[@trulylive9981]

Professor Swole

[@hamza_ME_]

If power of x and y and the term xy is same in nominator and the denominator, it will be homogenous equation.

[@zb5775]

A major zoo reported that a couple of their massive pythons were missing. Seeing Professor Leonard's arms and biceps, it is obvious where those pythons are hiding.

[@ahmadkarim1144]

my man you are built like a brick house, thanks for the lesson too

[@joeforshaw8362]

Another great lecture... teaching new things while doing a nice Calc II integration review.

[@hoomanyaghoubi5293]

thank you so much

[@leeprimeroessler3277]

1:04:20 About domain issues, should we not also include y/x != 1?

[@leeprimeroessler3277]

And one minute later, I realized that it is given by the x-y != 0. Always nice when I answer my own questions on youtube. No one else ever does it:-)

[@omiorahman6283]

Thank you sir

[@JB-in4dj]

There is a homogenous diffy q that is dy/dx =x+y that is very difficult to rewrite in that form. Do you have any examples of how to do that?

[@hansvangiessen8395]

just a linear DE: y' - y = x

[@ZackSussmanMusic]

thank you so much you made this make sense!

[@joobokjung]

Do you even lift professor?

[@MBULELo87]

clark Kent always does it or me ...from south africa

[@yashkapoor5894]

had no clue wtf these homogenous equations were before I watched your video. Thank you! P.S. I literally watched 3 other vids and still had no clue wtf was going on.

[@KundanKumar-jv6ku]

Nice lectures video sir