First order homegenous equations

[movcrit]

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

[akramunis]

are you supposed to know the F at the beginning or later?

[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!

[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

[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!

[moomilkboy]

@Hamshhi chicks are awesome but if i were him i would crazy from seeing so many every day lol

[Helfi92]

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

[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.

[ffx178]

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

[ad2894]

Ah I see :)

[ad2894]

Why is the constant not multiplied by the x variable at the end???

[arteeytube]

@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.:-)

[hurryupche]

do you raelize every government on planet earth can do that equation, and very little of them are 'g' masons

[giriisindahouse]

Its not an amateur mistake Sal bhai, I do it all the time.

[DTHRocket]

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?

[DonChedda]

@DTHRocket That is a Non homogeneous 1st order... Pay better attention to your teacher in class :P

[DTHRocket]

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

[tomasiscool]

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

[kourosh89]

@DTHRocket That's a Homogeneous Linear Equation, which Sal mentioned in the beginning of the video. I guess it's completely different from a plain old Homogenous Equations.

[kourosh89]

@DTHRocket nevermind. i think the +C makes it nonhomogenous

[Gearhe1d]

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

[MyOverflow]

Please tell me if I'm doing this wrong.

What I did was, instead of substituting after getting a function F(y/x), I just did this:

dy/dx = 1 + y/x, dy = (1+y/x)dx => y = x + yln|x| + C

y(1-ln|x|) = x + C

y = (x+C)/(1-ln|x|). I'm wondering if this is equivalent to what Sal got (xln|x| + cx).

[tucense]

@MyOverflow

dy = (1+y/x)dx Is not separable. Can't integrate both sides like normal without the v substitution.

[ATRXXRTA]

i hate that expression 'its trivial/it's not that trivial'. get on my nerves as hell.

[lianghaochen]

you sbelled homogeneous wrong..........

[lianghaochen]

@pasino0613 that was a joke, douche

[fuckyouallbitches1]

@lianghaochen what about sbelled lols

(Spelled)

[skyfaze]

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

[lianghaochen]

@skyfaze the c would become a function of x, ie: it would change if x changes.

[zalmaik1]

thanks man, really helpful

[ajhurliman]

To the best of my knowledge homo-jean-e-us refers to equations and ho-mah-juh-nus refers to dairy products.

[mjktrash]

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

[wufuhimself]

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

[Zalikify]

i love how he says homogenous)

[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

[mjktrash]

@mjktrash OOPS, who's the idiot now, apparently homogeneous and homogenous are different words...

[kamranyusuf89]

thumbs up

[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.

[themaheep]

@JackSouthernComfort That's what I thought too!

[UndeadTheta]

@themaheep x is a variable, so Cx would be a linear term.

[MegaJgar]

excellent, i was so confused about what is first order linear and homogenous and 2nd order, but you straightened that out.your videos are labeled properly.good job!

[pazerp]

Great video.

Straightforward example, nicely explained. Thanks, this helped me with something I'd been stuck on for a couple of hours.

[GinoftheWind]

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

[santimda]

Ehm... no, a constant C times x is a constant C times x... you can think of it as f (x) = C · x, it's a function of x, not a constant....

[SombraBlade]

Thank you for your teaching!

[peterfabbro]

this video helped me finish my exam at university :D

[GinoftheWind]

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

[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 !

[aqd2008]

Thanks for this video Sal, I was about to have a heart attack at 6:12 but anyway you realised it. Keep it up Mate

[gamr789]

please finish watching the video before commenting.. because he realises his mistake and correct it.. and yes.. xC cannot become just C because... C is an inmovable constant for that ecuation while.. X can take different values and the equation will hold right.. WildChildftw doesn´t know math or at list.. the antiderivatives..

[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!

[icafemoto]

and i know' you're not l337 at math cuz ur watching this fucking math tutorial video, ur just a stupid preteen trying to act smart. I'm the only genius here.

[icafemoto]

Woudn't the solution be y=ln(x)+xc ? not y=ln(x)+c ?

he forgot to multiply the c by x when he substituted for v? or..?

[WildChildftw]

Anything times a arbitrary constant is just another constant.

[icafemoto]

Hey, you're a dumbass. x is not a constant. x is a variable. x is not arbitrary. I'm right, this kid is wrong. Answer should be y=ln(x)+xc.  gg chump cake, no re.

[WildChildftw]

Thank you good sir. However your logic is horribly wrong.

For all real numbers x and C1, xC1=C2, where C2 is a real number. Mathematicians don't always bother writing superscripts for all their constants when in fact they are arbitrary.

[icafemoto]

it's pointless arguing with people with lower IQ than me because ur obviously wrong and have no idea what you're talking about. My math teacher and any math teacher would mark just +c wrong. it needs to include the xc because c is suppose to be a fucking constant. you can't have variables in a constant. It comes down to math orthodox.

If he was multiplying by a number like 5 to both sides, then yes u would be right, it wouldnt be 5c, it could just be C.

[WildChildftw]

Haha, I am having a hard time deciding if you are trolling or not.

What you are saying there is a logical fail. What if the x are given to be a 5? Or any other real number. Then voila, just a constant.

And btw, I study math at the university.

[powerfury]

Then maybe you should consider changing your major to something you can grasp. Like gardening.

[WildChildftw]

Yeah. Probably should change my major because of a fuckup in the comment field of youtube.

[powerfury]

Yes, that's what I said.

[WildChildftw]

Perfectly rational.

[tuxb0x]

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

[codenamecody]

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

[startvideo2007]

HOMO GENIUS !!!!! lolz

[dragonslight030192]

THANKS!! YOU ARE AWSOME!! LOVE YOU!

[soulflyfgm]

Keep it up!!

[CSULALS1]

excellent video. couldn't be learned any easier. kudos!!

[HelkaSilck]

Does the term "Homogenous" take on a different meaning when discussing 2nd order linear differential equations? In this video, you state that homogenous means that you can re-write it as a function in terms of (y/x), but in one of the "2nd order linear homogenous differential equation" videos, you explain that homogenous means that the funtion is equal to zero...

Am I misunderstanding this?

Thanks! Great videos!

[glykoulis]

great videos indead!

homogenous in greek means that they have the same parents somehow..

homo=same

genous=bread or genus

so it's like having a family of different functions.

in case of milk it is about chemistry and has the meaning that every spot in the milk seems to be the same.

in physics it is also used in case of magnets to declare that their magnetic field has the same intense allover.

finally in greek it is used to declare people coming from the same country,

[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.

[glykoulis]

I am afraid that homogenous magnetic fields have the same intense all over. It does not relate to the distance. Homogenous magnetic fields exist between two magnetic plates as far as I remember. : )

[aceofdragons]

No, you are not. The meaning of the word "homogeneous" varies in meaning when studying different classes of differential equations.

[mess1n]

homogeneous means that as the function y goes to 0, the sum goes to 0

[redstahr]

THANK YOU!!!!! you have no idea how much this helps!

[ltkenbo]

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

[Huetnak]

Hey! thanks for these videos mate, really helpful. im going to university in a few weeks so i need to catch up on this, as im studying electrical and electronic engineering. any chance you could make the reviews of the maths a bit slower and add in the description practical uses for the maths. that would be heroic. <3

thanks again.