@I Never Give Up! It doesn't matter if it's been 6 years. You watched the video recently, meaning it's still relevant. Anything added in the comments (like the other dudes timestamp) might be useful to future people who come watch the video, like you and me.
this is great stuff! someone tried explaining this with finding the integral of both fx(x,y) and fy(x,y) and then pulling out a definition for h(y) but this is easy to remember and much more effective KEEP UP THE VIDEOS!!
you should think on your own, khan does not want you to rot learn an algorithm that you can follow as soon as you see a problem, what is more important is that you should be able to conceptually understand it, and see how it works, general steps is something given by teachers so that students can pass easily in the exams without using there minds, khan gives much more than that, he provides the fundamental understanding of these complex concepts.
I just want to say what a wonderful job you are doing sal... I passed my calc 2 class with an A and it was partially because of ur videos. I watched all your videos for calc 2 and now i'm watching your differential equations videos. Your a great teacher keep up the good work.
Wow, i watched the whole EXACT EQUATTIONS tutorial. It was great. I actully understand it now. Way better than my math teacher who cant teach well. Thank You
I would just like to thank you! This example problem helped so much it is unbelievable. Everything is explained so well. Although my professor does something with putting My and Nx together by looking at the common terms. I believe your method is much more understandable. Thanks, again!
Thank you very much!! You saved me. I had a report to do about this, and a had a equation to solve and I understood nothing about it, but with your videos I was able to solve it. Thanks mate 👊🏻
I'm confused of last lines (after 10:20) you wrote dψ/dx = 0 which is wrong. Right way is dψ = 0. Consequences are the same. Nevertheless it was helpful for me, thanks
How did you determine that M(x, y) would be partially differentiated with respect to y, and that N(x, y) with respect to x? In my DE class we were presented with the equation in the form M(x, y)dx+N(x, y)dy=0, which would mean you always took the partial derivative of M and N with respect to the opposite variable of the derivative term. Basically I understand that M(x, y)dy should look like delM/delx because of the dy, but in your example I don't know how to make that determination.
Imao, this concept is no mystery to me. Because in my linear algebra and vector calculus class, we did something like that. We had to use it to determine whether a vector was conservative or not. Well thanks for the reinforcement. I have to take this differential class over the summer in 9 days so I am getting a headstart.
An arbitrary constant "+C" is included in f(y). For example, if f(y)=y^2 and you took the partial derivative with respect to x, then the answer is 0. If f(y)=y^2+C and you took the partial derivative with respect to x, then the answer is still 0. In first case, C was equal to 0, and in the second case, C is any number/constant.
@nejtilsvampe I know you asked this a long time ago, but Psi is an intermediate step to solving the Differential Equation in terms of x and y. Yes, it's preferred to solve for y explicitly, but sometimes it's hard so an implicit solution is okay. For example: Y = X + 1 is the same as 1 = Y - X
Question. How come at 1:39 you drop the y after declaring it as a constant, but don't do the same for the x^2 for the other function after declaring it a constant?
Q1. from "4:40" to "5:30", i don't understand why +C is replaced with f(y). And also i dont understand how when taking the partial derivative of f(y) will equal to 0 wrt x, if y is a constant wouldn't it still be f(y)? Q2. if we took the antiderivative of psi(y) would that "+C" be replaced by f(x)?
I would have done the partial integral to each of the equations(M and N Separatly) after finding they were exact. Then compared them to make them agree. Your methodolgy may also work though. Your way seems a bit convoluted to me.
So if our partial derivative of psi with respect to y is equal to N and everything cancels out, leaving f'(y) = 0, we can say that f(y)=C, and this is a different C than the one in the exact solution psi(x,y)=C? If this is the case, would it be best to define one constant as C, and the other as C' or even another letter?
Excellent video. However, at 11:12 you said that m is the partial of zi with respect to x and it should be with respect to y, as the derivative of cosx+2xe^y with respect to y is ycosx+2xe^y just like you put down and then integrated M sub y with respect to x...
@@Amin_3k hey that's awesome! I don't know a lot of people who would do med school because it requires a lot from you, so that's an accomplishment 😇🥳 I did chemistry a few years back and it was pretty hectic. Not as much of a pain to me as plane geometry though 😖 Glad you're doing good with your med school 😊😌
@@Amin_3k you're welcome 🙂 That was only high school so I didn't have a degree, but I finished pretty decent. Around a B if I remember correctly (that was my junior year around June 2018 or so) 😇
I think you are upset that someone has critiqued Khan Academy videos. I have simply pointed out something that would in fact enhance the effectiveness of the videos. It is not necessary to complain about this.
Because the derivative of psi wrt x is also equal to the initial equation (y*cos(x) + 2x*e^y) + (sinx + x^2*e^y - 1)*dy/dx which is equal to 0 as stated in the beginning of the video.
i dont understand why at 3:45 he says the partial of psi wrt x is equal to M, and why the partial derivitive wrt y is equal to N. I also find it confusing why he said the derivitive of psi wrt to x is zero, if right before that he said it was M. I know this comment is a month old, but if you got time would really appreciate the feedback
The partial of psi wrt x is NOT the same as the derivative of psi wrt x. When taking the partial of psi wrt x, we're treating y like a constant. When taking the derivative of psi wrt x, we're doing implicit differentiation. As for why the partial derivative of psi wrt x is equal to M, and why the partial derivative wrt y is equal to N, I’d go look at his videos called “Exact equations intuition 1 (proofy)” and “Exact equations intuition 2 (proofy),” because they definitely help explain where M and N are coming from.
why is the "derivative of psi with respect to x" equal to zero? Isn't the sum of derivative psi with respecto to x and derivative psi with respect to y equal 0, not just the first one.
The format for the first example is wrong. You should have dx multiplied by the M equation and dy multiplied by the N equation. So you have to do some rearranging to get it in the right format.
Two videos ago he defined psi = f1(x) g1(y) + f2(x) g2(y) + ... fn(x) gn(y) whatever happened to that? Is that a special case of an exact equation problem?
xoppa09 psi is just a name to a function. It doesn't need to be the same function all time. In the other video, he makes a general case for all the multivarible functions. I hope you understand ^^
Great job. Though handwriting is not too pretty yet could be complemented with the voice. And I must tell you that your videos are of reasonably low capacity. This one is just 5MB unlike other dopes. I discovered all these features later than I should have.
Respectfully, and acknowledging that this isn't the easiest thing to teach, this video is a bit "convoluted" compared to most of your other topics I've watched... If you have it in you, you might consider redoing these first couple of Exact Equations videos... Don't get me wrong, this and your other stuff is fantastic and you get my compliments, I just think these couple of vids went "off" here and there...
i dont get it, you never do anything with the y-prime stated in the first equation, N(x,y) is muliplied by Y-prime, but Y-prime never returns in the solution
Haha.. "my wife snuck up on me, I thought it might have been some critter or something".
That killed me
that reminds me on how lonely i am
I think he says “ or some shi-“ xD
3:04 got ya right here :D
well. why organic chemistry didn’t explain this 😭
i feel you bruh
😥😥
I feel you bruh (2)
I feel you bruh (3)
I know😭😭😭😭
it is -1. He corrects his mistake at 9:50. I guess a lot of people didn't watch the whole video ;)
9:05
@I Never Give Up! It doesn't matter if it's been 6 years. You watched the video recently, meaning it's still relevant. Anything added in the comments (like the other dudes timestamp) might be useful to future people who come watch the video, like you and me.
I cannot express my feelings man, u re perfect, greetings from METU 🇹🇷🇹🇷🇹🇷
this is great stuff!
someone tried explaining this with finding the integral of both fx(x,y) and fy(x,y) and then pulling out a definition for h(y) but this is easy to remember and much more effective KEEP UP THE VIDEOS!!
you should think on your own, khan does not want you to rot learn an algorithm that you can follow as soon as you see a problem, what is more important is that you should be able to conceptually understand it, and see how it works, general steps is something given by teachers so that students can pass easily in the exams without using there minds, khan gives much more than that, he provides the fundamental understanding of these complex concepts.
I just want to say what a wonderful job you are doing sal... I passed my calc 2 class with an A and it was partially because of ur videos. I watched all your videos for calc 2 and now i'm watching your differential equations videos. Your a great teacher keep up the good work.
Wow, i watched the whole EXACT EQUATTIONS tutorial. It was great. I actully understand it now. Way better than my math teacher who cant teach well. Thank You
I would just like to thank you! This example problem helped so much it is unbelievable. Everything is explained so well. Although my professor does something with putting My and Nx together by looking at the common terms. I believe your method is much more understandable. Thanks, again!
Sal for teacher of the Decade/Century!!!!
THANK YOU VERY MUCH , your work really helps me in my university and the way you explain D.E is just so great
Thank you very much!! You saved me. I had a report to do about this, and a had a equation to solve and I understood nothing about it, but with your videos I was able to solve it. Thanks mate 👊🏻
I'm confused of last lines (after 10:20) you wrote dψ/dx = 0 which is wrong. Right way is dψ = 0. Consequences are the same. Nevertheless it was helpful for me, thanks
Dude, you're amazing. I didn't understand how to do this at all 30 minutes ago, and now I not only know how to do it, I know why it is the way it is.
It's starting to sink in! 😮😊
How did you determine that M(x, y) would be partially differentiated with respect to y, and that N(x, y) with respect to x? In my DE class we were presented with the equation in the form M(x, y)dx+N(x, y)dy=0, which would mean you always took the partial derivative of M and N with respect to the opposite variable of the derivative term. Basically I understand that M(x, y)dy should look like delM/delx because of the dy, but in your example I don't know how to make that determination.
bruh just multiply everything with dx
@@starliaghtsz8400 unironically thank you lmao
@@CH-yp3km lol its ok
god bless you .you are the best.
fuk it's very hard for me
error 404 brain not found.
this is not easy for me to get a grip on but Im appreciating the pedagogical finesse.
Thanks alot
waah tnx for posting instructional videos of D.E ... it helps lots!!!!!!!!!!!!
Imao, this concept is no mystery to me. Because in my linear algebra and vector calculus class, we did something like that. We had to use it to determine whether a vector was conservative or not. Well thanks for the reinforcement. I have to take this differential class over the summer in 9 days so I am getting a headstart.
great man...
Great video for seeing an example from Boyce's Differential Eq.s book explained more fully ;).
An arbitrary constant "+C" is included in f(y). For example, if f(y)=y^2 and you took the partial derivative with respect to x, then the answer is 0. If f(y)=y^2+C and you took the partial derivative with respect to x, then the answer is still 0. In first case, C was equal to 0, and in the second case, C is any number/constant.
Totally illuminating DE's for me. Thanks!
khan is legend
very satisfying explanation
great teacher, better comedian haha 3:09
@nejtilsvampe
I know you asked this a long time ago, but Psi is an intermediate step to solving the Differential Equation in terms of x and y.
Yes, it's preferred to solve for y explicitly, but sometimes it's hard so an implicit solution is okay.
For example: Y = X + 1 is the same as 1 = Y - X
Question. How come at 1:39 you drop the y after declaring it as a constant, but don't do the same for the x^2 for the other function after declaring it a constant?
he didnt drop y at 1:39. he took derivative which is 1 and he didnt write since it is 1. but derivative of x^2 is 2x
love it .. thank you very much
Q1. from "4:40" to "5:30", i don't understand why +C is replaced with f(y). And also i dont understand how when taking the partial derivative of f(y) will equal to 0 wrt x, if y is a constant wouldn't it still be f(y)?
Q2. if we took the antiderivative of psi(y) would that "+C" be replaced by f(x)?
Why didn't you add x^2 * e^y y' to the Nx at 2:45. Isn't y a function of x??
i got it in the next video, thnx
I would have done the partial integral to each of the equations(M and N Separatly) after finding they were exact. Then compared them to make them agree. Your methodolgy may also work though. Your way seems a bit convoluted to me.
*MISTAKE*. At 8:50, f-prime of y is equal to -1 not +1
he corrects it 2 minutes later
Hey Sal, shouldn't you put "+C" at the end of psi at 6:40 ? Or is it included in f(y) ? Thank you!
So if our partial derivative of psi with respect to y is equal to N and everything cancels out, leaving f'(y) = 0, we can say that f(y)=C, and this is a different C than the one in the exact solution psi(x,y)=C? If this is the case, would it be best to define one constant as C, and the other as C' or even another letter?
this are event helpfull now, 13 years later from the day they were created
Excellent video. However, at 11:12 you said that m is the partial of zi with respect to x and it should be with respect to y, as the derivative of cosx+2xe^y with respect to y is ycosx+2xe^y just like you put down and then integrated M sub y with respect to x...
If i somehow manage to pass this test, it is going to be a miracle. I don't understand ANYTHING :(
Three years later but I hope you passed :)
@@nocturnalvisionmusic Well... i dropped out 😂😂 Im in med school now. Couldnt take the math in Chemistry 😂
@@Amin_3k hey that's awesome! I don't know a lot of people who would do med school because it requires a lot from you, so that's an accomplishment 😇🥳
I did chemistry a few years back and it was pretty hectic. Not as much of a pain to me as plane geometry though 😖
Glad you're doing good with your med school 😊😌
@@nocturnalvisionmusic Thank you my friend. Did you get your chemistry degree in the end?
@@Amin_3k you're welcome 🙂
That was only high school so I didn't have a degree, but I finished pretty decent. Around a B if I remember correctly (that was my junior year around June 2018 or so) 😇
Thank you bro
Tanx lott sir!!
where did the mines one go at 8:55 ?
He corrects himself later in the video.
u're the man!
Good tutoring
Awesome video>>>>
shouldnt f'(y)=-1 instead of 1?
thanks
so coool
Hello, is there a way to check if your function for c is correct?
@Pastafarealist thanks for clearing that up.
For partial of M ... why is cosx and 2x taken as constants? dont we have to differentiate cosx to -sinx?
12 years ago😱😱
Did you miss a negative sign for the f'(y)= 1 shouldnt it be = -1
He corrected it in 9:40
isn't that -y?
thanks!
For Ph
So is this "zie" the same as finding the general solution?
how do you check continuity? please reply
very nice
I think you are upset that someone has critiqued Khan Academy videos. I have simply pointed out something that would in fact enhance the effectiveness of the videos. It is not necessary to complain about this.
These are good, but I think it's time to update your DE sequence...
i know this is about making d(psi)/dx=0
but how about d(psi)/dy=0?
i think this is also possible? cause x is also function of y?
I am from LGU
f'(y)=-1 not 1 ?!?!?!
Sorry
how is derivative of psi wrt x =0 (video 3:30)pls answer!
Because the derivative of psi wrt x is also equal to the initial equation (y*cos(x) + 2x*e^y) + (sinx + x^2*e^y - 1)*dy/dx which is equal to 0 as stated in the beginning of the video.
i dont understand why at 3:45 he says the partial of psi wrt x is equal to M, and why the partial derivitive wrt y is equal to N. I also find it confusing why he said the derivitive of psi wrt to x is zero, if right before that he said it was M. I know this comment is a month old, but if you got time would really appreciate the feedback
The partial of psi wrt x is NOT the same as the derivative of psi wrt x. When taking the partial of psi wrt x, we're treating y like a constant. When taking the derivative of psi wrt x, we're doing implicit differentiation.
As for why the partial derivative of psi wrt x is equal to M, and why the partial derivative wrt y is equal to N, I’d go look at his videos called “Exact equations intuition 1 (proofy)” and “Exact equations intuition 2 (proofy),” because they definitely help explain where M and N are coming from.
My and Nx are not equal!! My has +1Xe^y but Nx has +2Xe^y
at 7:00 shouldnt the derivative for the f(y) be f '(y)(dy/dx)?
i cant read anything on this quality >_
I can perfectly understand on my macbook air which even has a low resolution
watch our videos ,we are recreating his videos in a great way
arent you in highschool? how are your eyes so bad lol
why is the "derivative of psi with respect to x" equal to zero? Isn't the sum of derivative psi with respecto to x and derivative psi with respect to y equal 0, not just the first one.
LOL @ 3:00 , priceless
The format for the first example is wrong. You should have dx multiplied by the M equation and dy multiplied by the N equation. So you have to do some rearranging to get it in the right format.
My wife???
yes i think hes married.
Please can someone explain why he put in f(y) instead of c. And can you also explain why we need to solve for it. It's urgent
Two videos ago he defined psi = f1(x) g1(y) + f2(x) g2(y) + ... fn(x) gn(y)
whatever happened to that?
Is that a special case of an exact equation problem?
xoppa09 psi is just a name to a function. It doesn't need to be the same function all time. In the other video, he makes a general case for all the multivarible functions. I hope you understand ^^
Great job. Though handwriting is not too pretty yet could be complemented with the voice. And I must tell you that your videos are of reasonably low capacity. This one is just 5MB unlike other dopes. I discovered all these features later than I should have.
Wait, didn't see that you corrected it.
I should start watching the whole video before asking questions.
its me the only one who gets lost with so many derivatives, anti derivatives, psi's, x's, y's ?
wait, how is Mx = Nx? when Mx = (cosx + xe^y) and Ny = (cosx + 2xe^y)
moses mccabe My = Nx. If he said otherwise, it was a simple slip up.
but (sinx+x^2 * e^y) is multiplied by y', you didnt isolate it from y'. :/
dont hate him--he just has a different take
At ~8:50, wouldn't f'(y) = -1 instead of 1?
Keep watching sal corrected it in the next step..
hi are you canadian
i thought there was a critter in my house for a second....ha!
Respectfully, and acknowledging that this isn't the easiest thing to teach, this video is a bit "convoluted" compared to most of your other topics I've watched...
If you have it in you, you might consider redoing these first couple of Exact Equations videos...
Don't get me wrong, this and your other stuff is fantastic and you get my compliments, I just think these couple of vids went "off" here and there...
this video makes me puke on differential equations more.Thanks Khan Academy
How is M and N exaxt if they differ with a ...1xe... = .... 2xe....
That's not the same equations.
what is ZII ...The answer proves what?
Couldn't u intergral N with respect to y. Wouldn't that be easier
240p video sucks. it used to be 480p... It's about as clear as soup youtube
Andrew Gallagher Yea, I know! It should at least be 480
watch our videos ,we are remaking old khan academy videos in a great way
My brain D:
Who's watching in 2024😅
😶14 years ago
do Wronksi please
ditto
i dont get it, you never do anything with the y-prime stated in the first equation, N(x,y) is muliplied by Y-prime, but Y-prime never returns in the solution
U choice one
there is a mistake in taking the differential of M !
It is a two!... he says that xD
it just looks like a 1...
@manny34711 yeah...
at 1:56 instead of 2x u wrote 1x
opps lol