First order homogenous equations | First order differential equations | Khan Academy

[@mikohayle]

The "+c" could have been put into the ln() by imagining it to be c= ln(A), where A is just another constant. This gives you a final answer of xln(Ax). That tidies it up a bit. Fantastic videos, keep it up!

[@tuxb0x]

I'm not too keen on Khan's description of homogeneous. I found the following description more intuitive. A function f(x,y) is homogeneous if f(x,y)=f(tx,ty). Thus, dividing the parameters of f(x,y) by x is sane and yields f(1,v) where v = y/x and y'=v+xv'. When substituted into the original dy/dx = f(x,y) equation yields v + xv' = f(1,v); a separable diff. equation. Thanks to sosmath for that explanation. Keep up the good work Khan!

[@MasterCarsReview]

It's been a while... thanks for the explanation!

[@DSEE-YamanSingh]

If the numerator function and the denominator function have the same degree in x and y, then it is a homogeneous equation. Thank me later.

[@FreemanTraceur]

*Last Year* Fine. *This Year* Thanks, man.

[@rickandelon9374]

Thanks mate , But i thanked you right after seeing the video!

[@boobooproductions1201]

Thank you so much

[@SoloPro]

im trying to cover this module in 4hours and it is actually possible with your videos so thanks so much! your a life saver... i think my lecturer will ask upto the first 15videos which ive nearly already done :D

[@hazuraharun3522]

still searching yt for math? does video from 2008 really help? YESS IT IS!!!!!

[@mashroom2927]

Haha same ad

[@thegreatxyz]

this should be uploaded in something higher than 240p =/

[@hotmandead1]

Agreed

[@denillaz]

it was 10 years ago dude

[@f129luke]

Man older than me

[@vestigialSmile]

144p?

[@thereynolds2725]

What does it matter? It isn't a movie. It's just text.

[@mariedrapalova7365]

Great, great, great! I could read the textbook over and over and it would take me so long to figure this out. It's actually not that difficult, I don't know why the textbook makes it so confusing.

[@hv30590]

homogenous comes from the greek word omogenis which has two meanings.. 1)something is evenly spread(as in the case of the milk you mentioned in the beginning) and 2) it is used to describe two objects which originate from the same thing or have some basic trait in common.

[@totasalam7060]

best teacher ever

[@nuttiBONG]

homogenous can have different meaning but in this case it is that the equation can be rewritten to be F(y/x) instead of just f(x,y). It can also mean that the equation is "= 0", there is a zero on the right side

[@mathalysisworld]

6:14 y = x ln|x| + cx

[@mathalysisworld]

oh, he later corrects!

[@CivilDefenseEngineer]

My teacher said a homogeneous equation was of the form A(dy/dx) + By + C = 0 Where A, B and C are constant coefficients. How does that relate to having F be a function of y/x?

[@jdkapit]

in the last step when you multiply the right side by x, why do you only multiply ln|x| by x and not c?

[@steffani8468]

Im more confused than i was 10mins ago

[@jasonvega9566]

LMAOO Real

[@movcrit]

Thank Khan, you just taught me solving diffy Q by substitution.

[@severrnijKGU]

you sir are the true and shining light for all differential equation students who meet the reality that DE tutors are non-existent. everybody talks about your name in my college's math rings.

[@043justdoit]

+ Cx in the end not just + C

[@emperorofthegalaxy1]

lol he corrected that at the very the end.

[@043justdoit]

emperorofthegalaxy1 I did notice towards the end, but I commented as soon as he forgot.

[@dogeness]

Then why not just delete your comment instead of replying to emperorofthegalaxy1?

[@justluigie]

i was just gonna ask that. lol I don't really listen to the video too much so i didn't know how he said it in the end.

[@asparwhite86]

nice. took me watching video, finishing and turning in homework and then watching this video again for me to get it... Probably helps that I am sober this time.

[@latergee]

how the hell do you do this in any other state except sober

[@ekoi1995]

3:55 product rule d(fg) = fg' + f'g

[@tuxb0x]

Khan corrects the solution at 6:42. You are right, the solution should be y=xln|x|+xc

[@Gearhe1d]

Thank you Sal! I aspire to be a mathematician of your caliber one day!

[@Alkatraz767]

did you do it?

[@ridoxi4341]

@@atilioantoniodadalto1648 bruhhhhh

[@Abdulrahman-t7v8v]

Thank you so much, Best teacher ever

[@Keletho]

i dontget why you decide to make y/x a substitution...thats really confusing you dont explain WHY

[@peter_castle]

***** It's a math trick. The reason is because you can prove, see the wikipedia article, that it works. You do it because it works.

[@mo-issa]

If you substitute the values of x and y with any number in both forms of the equation the results are the same meaning that you didn't change the value of the function but you rather manipulated the shape of by introducing a third variable that will help you reach the required for to integrate dx and dy It's basically like integrating by substitution

[@DosPerspectiva]

Because what we are dealing with is not a separable eqn in which we can integrate easily, we will first convert it. That's why.

[@Bader24K]

Thank you so much for this video it helped me a lot 😢

[@fermixx]

@GinoftheWind i thought it was an acronym, and i panic'd. Now i realize its just a process for cow milk. We dont call it homogenized in Argentina, we call it pasteurized. Anyways, thanks for the data, enough discussion about milk and cows for me. Btw, i passed my final exam, thank you khan !

[@Hamshhi]

Please apply to Asian University for Women as a Math Professor ASAP. The students would be really really grateful to a professor who explains like you! Thanks for the session!

[@p4Explosive]

I think you should be coming at this from the idea that V is the result of the function f(x,y) Then you can have a single variable to take the antiderivative of.

[@William_sJazzLoft]

Yo I like what you did in terms of the process, man. But I'm going to have to look up that definition for homogeneous. Excellent tutorial yo

[@patrickkhalifeh9858]

i might be late but here is your answer XD If the numerator function and the denominator function have the same degree in x and y, then it is a homogeneous equation.

[@user-bb5bf2tp4w]

6:13 shouldn't there be a Cx?

[@shayanmoosavi9139]

Did you even see the entire video :/

[@igotsth]

there is an e missing for homogeneous ;)

[@doysentidoatuvida]

it is because C is a generic constant that includes infinite posible values, so its the same write C than x*C cause xC takes also generic values

[@Daski69]

5:11 ... with regards to: I'd want to know about "if we multiply both sides by dx..." if that's correct terminology? I mean, dy/dx isn't really a fraction is it? I'm an absolute beginner to diff equations, I know the chain rule relatively well though and there I always pretend like I'm multiplying fractions: dy/dx = dy/du times du/dx so the du's cancel out... but is that really what's happening? What do the dx's and d's and such really mean? Thanks a million to anyone who can answer this!

[@robertbrandywine]

This has been discussed widely. You can check out discussions on math.stackexchange, but the simple answer is that dy/dx can be manipulated as if it were a fraction.

[@GinoftheWind]

Yes. The techniqual term for whole milk is homogenized milk-- homogeneous milk.

[@RalphThomasLibunao92]

@ad2894 Hey there! X was multiplied to the constant because we all know the "c" is any numerical value obtained from integrating a function of either x or y. Since we multiplied "c" to a variable "x", that does not yield a numerical value. It gives us a constant multiplied to a variable. It's like 3 multiplied to "c" is c while y multiplied to "c" is cy or yc. I hope i helped.:-)

[@Insano908]

does adding the x to the C at the end tho really necesarry? it remains a constant in the end anyway, that they idea of having C right?

[@awowoosas]

Yes it is necessary. If let say C = 2. It means that you will get 2X at the end. 2X is not a constant.

[@hereforgoodmusic]

Correct me if I am mistaken but since C is an arbitrary constant, XC could remain C as long as you recognize it if presented with an initial condition or any other case involving C.

[@jakedodsonjake]

If c is zero then yes, but you wouldn't know without initial conditions... so its not really arbitrary, because its a function of x, only if you were distributing a negative one would it not matter to change it to a negative constant, because it would still serve as a arbitrary constant.

[@tristan2668]

7:21 of youtube = 45 mins of class time??? How do you explain that equation? Please help

[@muhammadrumi6665]

It can also be done by ordinary differential equations

[@trevishaz]

Awesome teacher thank you

[@wufuhimself]

Is there an error at initial condition y(0) = 1 ?

[@mohfa1806]

nice videos ...thx very much...but what if v is a function of y and x ?

[@Ganjin88]

Yea i see what you are saying but intensity of the magnetic field weakens as you move away from the source because the magnetic field will produce a weaker force on particles that are very distant away from the source. But good analysis though.

[@Helfi92]

I love you khan Academy!!!! (no homo) I wish my professor explains like you.

[@codenamecody]

thanks these help a lot, my diffy Q teacher only speaks engrish

[@ruthsarange2056]

NYC... atleast I can understand math modelling

[@mjktrash]

Why (at ~3:50 => ~4:00) is y=xv used as the basis for dy/dx?

[@g_dust]

At the end you say it was seemingly inseparable? But in the beginning you say it would be easy to solve by separation?

[@JackSouthernComfort]

Wouldnt 'XC' just be C. Your multiplying a constant, so it would just end up as another constant. This is what Khan has done in the previous vids. Many thanks for the videos, they're a great help.

[@sullivan3503]

x is not a constant, so it cannot be absorbed into another constant. x can be any (usually real) value.

[@mitch7w]

So helpful. Thank you.

[@varunjain7538]

Can the degree of homogeneous function equation be negative or fraction

[@alfonso8667]

kudos to the same guy who teach me through youtube vids "khan academy and other indian mathematician utubers" *F*

[@MahmoudGamal-io3hl]

I don't know why I laugh when he keeps saying "Homogenous"

[@huynhtatthang6754]

always the best!

[@leenhamdan1007]

Thx🌸🌸Dr

[@skyfaze]

does it really matter at the end because c is still a constant

[@tempneff]

Hey Khan, Where can i find reference of that way of checking for homogeneity 'F(x\y)'? I can't find it in any textbook nor any formal definition that includes it. Thanks

[@yash1152]

6:41 kinda semi-strange that i made the same mistake even before watching the solution

[@Aisyah-qf2pz]

Thank youuuuuuuu.

[@aimansaffuanamri4601]

I thought c is just a constant? why does it have to multiply by x?

[@robertbrandywine]

Because he multiplied both sides of the equation by x. When you muliply ax + c by x it becomes ax^2 +cx.

[@JasonWilliams89]

@@robertbrandywine But cx is literally the same as c

[@zaeny]

This is what happens when you don't finish videos on KZbin. Your Mathematics teacher would be disappointed.

[@GinoftheWind]

Isn't a constant C times x still a constant C?

[@k.manjericao1583]

not at all. Absoletely not. X is a variable still.

[@k.manjericao1583]

sorry, definitively you already know that, 10y ago.... xD

[@TheCrazyheat]

Who needs lousy graphs when he is explaining all of it so clearly

[@MrCuteguylol]

arent you like, supposed to tell us WHAT is a homogeneous eq instead of how to solve it?

[@XxGrandSTORMZxX]

thisss

[@MrCuteguylol]

actually i figured it out incase you dont know, homogeneous equations are equations where the degree of numerator and denominator are the same. When the degrees are same, you can take the highest degree of x as common from numerator and denominator and they can cancel out since they are terms of x of same degree. Therefore you can make a function of y/x using this. I figured it out later on lol but it would have been easier if it was included in this lecture

[@XxGrandSTORMZxX]

+MrCuteguylol Thanks for this info. But how did you figure this out? The way it was presented in my class was that homogeneous equations are equal to 0 on the RHS

[@MrCuteguylol]

Actually by definition: f(tx,ty)= (t^n) f(x,y) ; t is a nonzero real number And yes it can be written as M (x,y) dx + N (x,y) dy = 0. But the problem with this is that this is also true for an exact equation. I told my students the previous definition because it is very easy to change that into f(y/x) if you just see the homogeneity of the equation by simply saying the degrees are same. What you have been taught is also true but in my opinion it can confuse the students when they start studying exact equation and non exact equation and when you convert the non exact into an exact one.

[@MrCuteguylol]

Since it merges two concepts into one. A student must be able to identify one from the other

[@miroslavkovac2159]

hi can you do and help me with something like this.. i have no idea how i should progress on it. In book it says that it is homegenous equation but i can t solve it.. the equation is: ((2x + 3y) / (3x + 2y + 1)) + y` = 0

[@jamellyfreitasferreirajame2109]

Thanks a lot!

[@purenada]

really helpful

[@outrivaldynasty1672]

what is the meaning of "Homogeneous equation" how do we know its homogeneity? please help Salam and love from P A K I S T A N

[@peterfabbro]

this video helped me finish my exam at university :D

[@aboudiozil302]

it one of the best video

[@eddythinman]

Is it me or does his voice/ mannerisms remind you of Brandt from the big lebowski... "without the necessary means for, necessary means for a proper education. Don't touch that"

[@rogerodipo3499]

Great man. I thoroughly appreciate. Also its a homoGENEous differential equations. Its pronounced different too! :) Thanks.

[@robertbrandywine]

Isn't it pronounced homo genie us? But most people got it wrong through the decades and now most people spell it homogenous and pronounce it that way, too, with the accent on the mo syllable.

[@Ahfjo]

Khan used that trick in part 2 to this lesson. He just wrote ln|C| in the next video.

[@Andrew6James]

Can someone explain why Y=vx? Why was V treated as a function of x and not a constant. -A-level math student

[@FernandoRodriguez-ge2tg]

Andrew6James if you don’t know that y = vx because v is defined by v = y/x you shouldn’t be an “A-level math student”

[@Andrei-ds8qv]

ty!

[@Mustafa_c99c]

Thanks

[@muhammadrizaldifarsah4233]

I almost wanna correct you on that mistake hahaha thank god u realise before I'm going berserk hahaha

[@SK-ps6lp]

I've been doing this for so many homogeneous problems and cannot seem to get the answer

[@ffx178]

haha my friend always used to called it homo equations even in class room

[@hytk6481]

I want to know HOW to tell if it's homogenous... not how to solve it.

[@Mega2Sakaura]

does it have to be y/x?

[@funcionamaldito]

it can be x/y

[@mo-issa]

But if x/y It has to be dx/dy

[@ltkenbo]

Awesome! Your great at explaining all this! wish you were my teacher!:-)

[@kaisel4161]

Hello...I am a being from the future

[@Vlad.007]

@@kaisel4161i m even more from the future 👀👀

[@negevherbals6891]

This is beautiful.

[@AlChilazoLife]

Keep it up!!

[@Sam-dc9bg]

Nice.

[@TheDizar88]

hahaha... amateur mistake... nice joke bro...

[@patrickkhalifeh9858]

my head hurt when i saw him just writing C without x i thought i didnt know math at all

[@CivilDefenseEngineer]

@DonChedda Actually, that's what he said. So if I'm wrong, he's wrong.

[@tohjinghui9787]

thank you:DD

[@tomasiscool]

@DTHRocket "I will now introduce you to the idea of a homogenous equation..."

[@dalenassar9152]

Sal, It is NOT "homogenous" it is "homogeneous", pronounced: HOMO-GE-NE-US. I guess your teachers pronounced it incorrectly, since you are the type not to be wrong out of thin air. Also, "EULER" is pronounced: "OIL-ER". My differential equations teacher taught me that the proper spelling of "SOLUTION" is NOT "SOULTION", A lesson I will never forget. My science fair judge taught me that "ENERGY" is not spelled "ENRGY". I will always believe a great teacher will go the extra bit and not ignore things like this!

[@pevreka]

you didnt explain what homogenous is

[@xoppa09]

does anybody know why the transcript is in arabic by default

[@MaheepSingh12]

@JackSouthernComfort That's what I thought too!

[@AHS1373]

homegenous?

[@gonzalodiaz9590]

buena calidad gp

[@schackproffset]

@tristan2668 it is a first-order equation, solve it!

[@akeemroberts5722]

1080p FULLHD

[@kaushikrj5909]

16 years ago :(

[@JohnM...]

the word is HOMOGENEOUS - Not homogenous

[@dr_rich_r]

Thank you! No one says it correctly anymore.

[@vicyang4141]

LOL

[@jeremiahtsosie656]

Mathematicians...right?

[@mjktrash]

@Zalikify "Ha-ma-na-jous" or "Homo-jean-e-ous" I grew with the first pronunciation where as all of the idiots at CSU in Colorado say the second... lol

[@KamranYusuf]

thumbs up