The differential equations videos seem almost complete, but it needs a few more tricks. Like substitution tricks when even the integrating factor method doesn't work, or the Bernoulli equation method. It would be nice to see them added.
I don't know if this is even useful for you now but maybe someone watching this like me after this will get the same confusion. The answer is that while finding integrating factor we don't take integration constant. It was taught to us in 12th standard by our math teacher. I, however, don't know the reason myself. He just told us to do so.
I don't know if this is even useful for you now but maybe someone watching this like me after this will get the same confusion. The answer is that while finding integrating factor we don't take integration constant. It was taught to us in 12th standard by our math teacher. I, however, don't know the reason myself. He just told us to do so.
@@aloofakeelah2695 The reason is nothing special. You only need one candidate function which can work as the integrating factor. That’s why any single solution is okay. You don’t need the whole family here.
I may be years late to some of you, but you need to watch the previous videos from Sal's diff eq series to get a better context of where Sal is coming from in this video.
maybe if one day I suddenly burst into existence as an accomplished mathematician or physicist? Yes, I can only hope that this happens through some artifice of industry.
Sal, I really admire ur work,and i have a question why u didn't differentiate y',Isn't a function of x?!! so why did u ignore it when you differentiate with the product role?!!
u don't understand me.if u took the y' with respect to x then the product is a function of x,if u take the derivative of y' with respect to x then its y'' that what it should be but he ignore it like if y' is just a constant,yet it is a function of x.so i see that he should have taken the second derivative instead of deal with it like it just a constant of something other than x.
Plaq1423 in simple words, partial derivative of a function of x and y wrt to x is simply differentiating wrt x treating y as a constant.. similarly, partial derivative of a function of x and y wrt to y is simply differentiating wrt y treating x as a constant.. fr instance, if f(x, y) = 2x + 3y then its partial differential wrt x is 2 (treating y as a constant) and its partial differential wrt y is 3 (treating x as a constant)
@watscrick cause the derivative of the left hand mu(x) with respect to y is zero so if you do the product rule, it will be just mu(x)(3x+2y) + (0)(3xy + y^2) so just cancel it out.
Hi, I just wanna say great job. I'm ganna take this analysis class using the same textbook but in ninth edition next semester. And when you take the partial derivative of N with respect to y, shouldn't it be (2x+y+xy'), consider y is a function of x?
no because it s a partial derivative so only explicit dependence matters khan has some good multivariable calc video's they should clear help clear it up
I know you said this a year ago, but if you're still interested, when you're finding an integrating factor, (using this method or otherwise) you're finding AN integrating factor. You don't necessarily need all of them, but obviously if you solve for mu you're going to get all possible equations just as with any other DE. In this case though, it is mu=c*x, not plus. mu=x is chosen for convenience.
Please help... I checked online for this question and every site(more than 5) I checked did not solve this using integrating factors, they all treated it as a linear homogenous equation and well, the answers you got and that which they got are different(tid-bit). I need Clarity ASAP. Thank You very much!
Why does mu(x) remain mu(x) when you are taking its derivative with respect to y? Additionally, if mu can be a function of x,y, or x and y, how do we know that there isn't a y in the function mu? If there was a y, then shouldn't taking its derivative with respect to y give you something? That part confused me. Also, why didn't Sal do the product rule for the left-hand side (our new M) but did do the product rule with the right-hand side (our new N)?
So during the solving of the integratorion factor and since at the end of the video since we have to integrate it, than we discard the constant of integration? "im talking about the last equation that you immediatly concluded that miu=x"
sir Please tell me how to use method of inspection to reduce diff.. equ.. in exact form.how to reduce this differential equation (2y+6xy²)dx+(3x +8xy²)dy =0 in exact form
@knighttango : my book reads: Existance of an integrating factor: "If a non exact differential equation has a general solution F(x,y) = C, then it has an integrating factor" So that theorem is just a piece of shit, and i never used it. We are fucked up..
![I.N "HALLUCINATION" | [Stray Kids : SKZ-PLAYER]](http://i.ytimg.com/vi/n5B5q1Hwt_U/mqdefault.jpg)
I am watching it 14 years after it was published. Thanks Khan Academy
i was 2 years old then now I need this
I'm watching 15 years after so I'm better than you
@@omniyambot9876 why does a 16 y/o need this? Isn't this for University students?
16 years
Beauty of mathmatics. There are more 12-16 year olds watching these than you think.
As a business student, you'll find that, no matter what university you were admitted to, you're actually attending Khan Academy ;)
As an engineering student I'd have to agree with you lol
@@rdyjur As a math student, I'd agree with you both lol
as a student (with the possibility of failing this term), I have to agree with all of you
after 8 whole years you posted lemme answer mr/mrs buisnessman as a physics student i've gotta agree with both 3
@@StarPassenger1 me too
almost 6 years later, and we come back to this. Thank you KHANNNNNNNNNNNNNNNNNN
almost 10 years later, I come back to this. Thank you!
Yet i am here
amen
Passing by...
I am in 2019, it is almost 13 years later.
After 15 years. Thank You.
If you have time, I recon you should redo this video in higher quality. It would be very helpful
watch our videos ,we are remaking old khan academy videos in a great way
It's a homogeneous equation. So put
y=vx solve in an easy way.
240p....rip.
Not alone
What do you expect uploaded 13 years ago
You have boosted my passionate love for differential equations sir. Keep it up.
Maybe I have been studying too much, but I giggle everytime you say "mu"
Pro trick : watch series at Flixzone. I've been using it for watching all kinds of movies lately.
@Alan Cairo yup, I've been watching on Flixzone for years myself :)
Crazy to think that people like you knew how to do this pristinely while I was still learning long division and basic functions
I had just started school when this video was uploaded and now this is the final chapter of my maths in my last few months of school.
@@peeper2070 oh, you could've watched it when you started school then 😂 would've been very helpful.
To solve equation only by integrating factors we need two of them
This equation is also homogeneous and we can easily find another integrating factor
I've not been taught this method of integrating factors. Because of thethe differences in methods hard to really tell what is happening in either one.
This is kind of an odd way of doing integrating factors. I've never seen it done like this.
Thanks khan Academy..It helps me night before exam😁
Sheikh M K Rifat how did you do on the exam?
@@Paradox586 Great man
Why do you not allow the y' to differentiate?
At 1:35, he underlines x^2+xy but why doesn't he underline the entire thing being (x^2+xy)y'?
it seems he just did it without much reason
1:10 ain't this also a homogenous differential equation - each term has same power?
The differential equations videos seem almost complete, but it needs a few more tricks. Like substitution tricks when even the integrating factor method doesn't work, or the Bernoulli equation method. It would be nice to see them added.
Amazing brother! I am watching in 2022.
sem vruhh🤝🤝🤝
thanks to you ! could not get where this factor comes from
When integrating 1/u and 1/x on both sides aren't we left with u(x) = x+c?
Where does the constant c go?
Faaiz Haque I’m confuse about this same issue tooo
Its actually unnecessary, as we only need the solution to the integral, which gives us the integrating factor.
I don't know if this is even useful for you now but maybe someone watching this like me after this will get the same confusion.
The answer is that while finding integrating factor we don't take integration constant. It was taught to us in 12th standard by our math teacher. I, however, don't know the reason myself. He just told us to do so.
I don't know if this is even useful for you now but maybe someone watching this like me after this will get the same confusion.
The answer is that while finding integrating factor we don't take integration constant. It was taught to us in 12th standard by our math teacher. I, however, don't know the reason myself. He just told us to do so.
@@aloofakeelah2695 The reason is nothing special. You only need one candidate function which can work as the integrating factor. That’s why any single solution is okay. You don’t need the whole family here.
why is it in 240p?
I may be years late to some of you, but you need to watch the previous videos from Sal's diff eq series to get a better context of where Sal is coming from in this video.
Yaar yeh banda cha gaya hai :-)
9:42 u(x) = 1/k x
Bernoulli Method would be useful too.. just a couple of examples would be good. not asking for much. thanks mr.Khan :)
Can you use this trick to solve all first order ordinary differential equations?
@5:19, why didn't you use implicit differentiation =S???? at the end (checking solution) of the previous video, you used implicit differentiation
Thank you so much!!
Seriously, these videos are so good!! Thank youuuuuu!!!!
KHAN You are The best RUclipsr :)
i don't think so, only a very small class of ODE is solvable exactly.
One of the oldest comment bro, love you, seeing in 2022💖👍
maybe if one day I suddenly burst into existence as an accomplished mathematician or physicist? Yes, I can only hope that this happens through some artifice of industry.
in the end when you get dx/x=dμ/μ if I'm not mistaken you shouldn't say that x=μ, but |x|=|μ| which is not necessarily the same. Picky me lol
Sal, I really admire ur work,and i have a question why u didn't differentiate y',Isn't a function of x?!! so why did u ignore it when you differentiate with the product role?!!
he is taking the partial derivative so you only count explicit dependence khan has god muti variable calc videos they should clear this up
u don't understand me.if u took the y' with respect to x then the product is a function of x,if u take the derivative of y' with respect to x then its y'' that what it should be but he ignore it like if y' is just a constant,yet it is a function of x.so i see that he should have taken the second derivative instead of deal with it like it just a constant of something other than x.
What if there is an integrating factor shown like a function, for example m=f(x+y^2) for this equation (3y^2-x)dx + (2y^3-6xy)dy=0
Is there an explanation of Integration Factors that does not make use of partial derivatives? (I have no idea what a partial derivative is.)
as far as i know there is no way to solve this without using partial derivative
A partial derivative is a 3D derivative. Ex d/dx[x^2y2*e^iy+ y]
Plaq1423 in simple words, partial derivative of a function of x and y wrt to x is simply differentiating wrt x treating y as a constant..
similarly, partial derivative of a function of x and y wrt to y is simply differentiating wrt y treating x as a constant..
fr instance, if f(x, y) = 2x + 3y
then its partial differential wrt x is 2 (treating y as a constant)
and its partial differential wrt y is 3 (treating x as a constant)
Do u remember this comment
@watscrick cause the derivative of the left hand mu(x) with respect to y is zero so if you do the product rule, it will be just mu(x)(3x+2y) + (0)(3xy + y^2) so just cancel it out.
you make calculus easy
The example taken by you is also a homogeneous equation...so we can find integrating factor in other way also??
Oh yes, the videos from 2007 are really helping.
I love your video's, very helpful
What if in solving for the 'mu' the equation didn't simplify to get a function in terms of x only. That is we still have y in there
dude, you're awesome!!!
I have to say this problem worked out very...conveniently. Usually stuff won't be able to cancel out like that and turn into such a simple D.E.
Which piece is the integrating factor?
I can find (x) with out using u (x) in short time and easy.
Excellent
Okay the examples have to be much easier than the sums I have to solve, I understand...
COOL TY!
This makes my d.e complicated.hmm
Hi, I just wanna say great job. I'm ganna take this analysis class using the same textbook but in ninth edition next semester. And when you take the partial derivative of N with respect to y, shouldn't it be (2x+y+xy'), consider y is a function of x?
no because it s a partial derivative so only explicit dependence matters khan has some good multivariable calc video's they should clear help clear it up
Try solving this: y(1-xy)dx + xdy = 0.
I know you said this a year ago, but if you're still interested, when you're finding an integrating factor, (using this method or otherwise) you're finding AN integrating factor. You don't necessarily need all of them, but obviously if you solve for mu you're going to get all possible equations just as with any other DE. In this case though, it is mu=c*x, not plus. mu=x is chosen for convenience.
You're looking for any integrating factor so take the constant of integration to be 0
you multiplied the two functions by (x) but it doesn't look like you only use (x) ? in the minute 1:15
do Wronksi please, i will try to post this on every video sorry :)
thanks a lot
Thanks Sal. But couldn't Mu also equal negative x? Since there were supposed to be absolute values?
wonderful! thank u
Sir give me an example of non exact differential equations in which all five rule fail ,integration factors fail??
Great
Surely mu actually equals x plus a constant, not just x
Please help... I checked online for this question and every site(more than 5) I checked did not solve this using integrating factors, they all treated it as a linear homogenous equation and well, the answers you got and that which they got are different(tid-bit). I need Clarity ASAP. Thank You very much!
so did u get it cleared? If yes, please let me know
Why does mu(x) remain mu(x) when you are taking its derivative with respect to y? Additionally, if mu can be a function of x,y, or x and y, how do we know that there isn't a y in the function mu? If there was a y, then shouldn't taking its derivative with respect to y give you something? That part confused me. Also, why didn't Sal do the product rule for the left-hand side (our new M) but did do the product rule with the right-hand side (our new N)?
If Nx which was u(x) x (x^2 + xy) x y' = 0, then should this equation be equal to zero because the whole argument is multiplied by y prime?
So during the solving of the integratorion factor and since at the end of the video since we have to integrate it, than we discard the constant of integration? "im talking about the last equation that you immediatly concluded that miu=x"
DRoque14 yes. C only comes in at the end. not a part of Miu
Are exact equations the same as Linear equations?
At 7:02 , shouldn't it have become U(x) (x+3y) = .... or am i mistaken? thanks!
i have a question, what if theres a function of y but u assumed that the "mu" is only function of x. sorry for my english..
Haven't done partial yet......
what if we suppose μ is a function of y?
at last integral 1/x = 1/u, shouldn't u = +- x? or this doesn't matter?
Does it have to be homogenous?
+joshua morales if its not homogenoes the solution of the non homogeneous is the solution of the homogenous plus a constant
is there any short cut way .in solving problem like this?
nice
thankssssssssss
These old KA videos kinda wonky ngl
absolutely beautiful
sir Please tell me how to use method of inspection to reduce diff.. equ.. in exact form.how to reduce this differential equation (2y+6xy²)dx+(3x +8xy²)dy =0 in exact form
12 years ago🙄 wow
Resolution is unsatisfying
wooooow
Could someone please explain to me why My has to be equal to Nx to have the function a differential one ?
Then the equation will be exact.
Sal you are god
Differential equation has infinite integrating factors. Why? Can some one explain.
How come we are not using e^(integral of P(x) dx) as the integrating factor?
Because that's another method that's shorter. He's showing one way to solve for it without a formula
@@dg_dmtll Thanks man.
beautiful, just beautiful
2018?
@knighttango : my book reads:
Existance of an integrating factor:
"If a non exact differential equation has a general solution F(x,y) = C, then it has an integrating factor"
So that theorem is just a piece of shit, and i never used it.
We are fucked up..
where u started using yellow colour ,it confused me what had u done in that step
What happened to the y' ???
Hello! Can you help me in solving this differnetila equation solve y'=(y^2)-1?
You are saintly.
where did y' go?
Sal. μ is coming aut to be xc why is contant not taken into consideration.?
I am gonna fail. Pray for me.
What if (x+y)=0, can it be divided by both side at 7:53?
they x=y so you are only excluding that trivial solution
I have simpler way to solve this example and other examples !!!
my head hurts