First order homogenous equations 2

[subhaniawan]

sir i owe you my grades , thankyou so much

[Dunnylaaaaaaaaaaaaad]

I think the line at 3:43 is wrong, because he says to bring all the v's to one side, when he brings the 1+v^2 over.. why does the equation equal to 1?? should it not equal to 0?? Should he not just bring the v^2 over and leave the 1 where it is???

[Exploratorius12]

@Dunnylaaaaaaaaaaaaad he brings all the 'v's to the left hand side by dividing both sides by 1+v^2. thus the right hand side becomes (1+v^2)/(1+v^2) which is 1.

[add1c7i0n]

youre such a G khan. love u buddy

[chemicalsymphony]

how is the anti-derivative of 2v/(1+v^2) = ln(1+v^2)?

[shapeurmind]

@chemicalsymphony I don't understand it either. I got 1/2 ln(1+v^2) .....

[Exploratorius12]

@chemicalsymphony notice that you get the enumerator if you derive the denominator: (1+v^2)' = 0 + 2v = 2v

so basically you got something like f'(x)/f(x) with f(x)=1+v^2 and f'(x)=2v. it happens that ln(f(x)) is its 'anti-derivative' why? well if you derive ln(f(x)) by using the chain rule you get 1/f(x) * f'(x) which is the same as f'(x)/f(x). so the solution is ln(f(x)) which is ln(1+v^2)

[AllRiffRaff]

@chemicalsymphony because if you substitute (1+v^2) with lets say "u". equation becomes (2v/u)dx. so u = 1+v^2. differentiate this you get du/dx = 2v, then du = 2vdx. then equation becomes (1/u)du. which you integrate to become ln(u). substitute 1+v^2 back in for u and you get ln(1+v^2)

[JCP598]

Why is the term (2 x v v´/1+v^2) in 3:55 equal to 1 and not 0? That´s the only point I´m not getting in this video :( Other than that THANKS! You´re saving my engineers career. It´s just frustrating when teachers talk in their own math terms and you don´t get a thing of an actually understandable problem. Thx!

[abhi99ps]

I think we can simplify the result into y-x sqrt(Cx-1)

[leahrr]

its more complicated than what i knew

[Aznproz]

wow, this is so sad!!! I read the book, prof's note!!! all their explanations were just F(tx, ty) = t^(alpha) F(x,y) And i did not understand a thing!!!!! After these 2 vids about homo. eqn made by an awesome guy named Khan!! it instantly made so much sense to me!! XD hope i do well at tmr's midterm!! :D keep up the good work man!

[Shmml]

Thanks!

[doubleja]

"This is where we just put our Algebra hat on." ^_^

[Germs9592]

This helped A LOT!!!!!! Been watching your calc videos. WAY better than MY teacher at school :/

[iwantthis22]

thanx a million, it made my day

perfect explaining

[iwantthis22]

thanks a million, it really made my day =)

[lirongolan007]

huge thanks ftrom Israel!!!

you are the best!

[psychojoshie]

Ahh, I'm sorry but I don't get how you could change the constant C -> ln|c|. Because the ln|c| can only be positive numbers. But then C could be negative, right? Can someone enlighten me!?

[337punter]

@psychojoshie: because it is the natural logarithm of the absolute value of C, it can also only be positive.

[BannedLol4l]

@psychojoshie I know it's been a year but whatever...

ln|C| actually can take on any value between -infinity and +infinity, because the range of the ln|C| function is all real numbers (graph it).

[letmego11]

In all these videos so far, you were trying to figure out what y (the original) function was. But in this clip you wrote the solution in implicit form while you could have written it in form of function y! Is there any specific reason behind that? Can you explain a bit more? I am confused! thanks

[neoYTPism]

At 7 minutes in, how come you didn't keep cx in absolute value bars when taking them out of their logarithms?

[disornr]

I love you so badly SAL!! You are the man!!

[purplemjhope17]

thank you sal :)

[blarfsgnarg]

you are my IB HL maths options paper savior!

[S41YAN]

hey

[lauralew2222]

How can you tell the difference between a homogeneous DE and an exact DE when they are not in their usual forms by looking at it right away?

[daghnl]

This man is a champion.

[GinoftheWind]

Thank you! This second example really cleared things up!!

[Geckuno]

Of course no one cares about the spelling etc. but it is just a comment and thinking that these videos are watched by not just Americans but by lots of other people from around the world (like me) it shouldn't be considered as a swear if somebody tells that the spelling is wrong. It is just a comment to make the other videos better. and btw thanks Khan you have been helping me for like 3 months now :)) big fan

[zachattack300]

thank you thank you thank you :)))) got a prelim in like 2 days

[PrinceFX]

AWESOMENESS!!!

[ad2894]

isn't it homogeneous? Doesn't homogeneous have a different meaning?

[DLag81290]

Very Helpful! thanks!

[vertthrasher]

Wow, Penn State sucks... There is so much stuff in all of these videos that we never covered in my ordinary / partial differential equations class. Exact equations, never covered. Integrating factor (using mu) never covered. [we did cover, however, using e^int[P(x)dx] using diffeqs of the form y' + P(x) y = Q(x) . Totally different than the way he showed. ]

[aymric]

Really? That's pretty shocking. I'm taking Diff Eq at a community college. We're only a month into the course and we've covered all that. It was on the first test even.

[fermixx]

ppl arguing about pronunciations are those who are not paying attention to the subject itself.

to be honest, my mind is focused on dif eqs so actually it doesnt matter how he pronounces/spells words. Im focused on the numbers instead !

something wrong in the numbers would be something to discuss here, because its what really matters here

[styleguru1986]

@fermixx hello Mr. Salman Khan , i first of all thank you for ur great help .

I have a question and i need its solution plz help me , the question is

y=(1+p)x +p^2 ; where p=y'

[fingerboy18]

@fermixx Yeah, some people get all pissed when others say "diff-ren-tial" instead of "diff-er-en-tial". I say: who cares as long as you understand!

[vtec917401]

This is very very helpful!

[autorancho]

Perfect, Thanks !!!!!

[bennyripped]

this isn't an english class.

thanks for your video it has been amazingly helpful

[atoponce]

english isn't the only subject where pronunciation and spelling are important.

[cyprus2k11]

FACT: the people watching, care more about understanding the subject, which he does a good job explaining, and very few to none give rats about some english word pronunciation

[atoponce]

Dude. It's pronounced "hoe-moe-gene-ee-us" and it's spelled "homogeneous". It is not pronounce "hoe-mah-guhn-us" and it is not spelled "homogenous". It contains 5 syllables, not 4, and the spelling contains 2 e's, not 1.

FYI.

[Mach245]

i dunno about u but in the US (UIC) its pronounce ho-mah-gi-nous

[xxdeetsxx]

Does it matter?

[OneRadVideo]

Wow, really good explanation... Thanks!

[cwxzeng]

Thank you

[rylan1000]

brilliant explanation

[nebula1230]

Neatly explained.... Thank you very much..

[supunnba]

nice work.... i'm getting flashbacks when i see these... it'll really nice that i could re memorize all the work by watching these videos on your channel.

[wilsondirt]

Hi Sal,

I have a question about the first step to this example:

Did you determine that both top and bottom had to be multiplied by

(1/x^2) because of the highest order (in which this case was 2nd order [y^2])?

Wilson

[hasnainkhatau]

@wilsondirt you always divide by the 'degree' of the homogeneous equation. In this case it was 2nd degree (the sum of the powers in each figure was 2)

[gambuzo]

Fantastic, thank you !!!

[gamemaster014]

omg thank you for clearing this up ive been having trouble on homogenous equations thanks sal