Exact equations example 1 | First order differential equations | Khan Academy

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  • เผยแพร่เมื่อ 5 ม.ค. 2025

ความคิดเห็น • 188

  • @haroldh6678
    @haroldh6678 6 ปีที่แล้ว +187

    Haha.. "my wife snuck up on me, I thought it might have been some critter or something".
    That killed me

  • @Pages_Perfected
    @Pages_Perfected 4 ปีที่แล้ว +208

    well. why organic chemistry didn’t explain this 😭

  • @tristan2668
    @tristan2668 11 ปีที่แล้ว +64

    it is -1. He corrects his mistake at 9:50. I guess a lot of people didn't watch the whole video ;)

    • @kleenexpresslaundrette2218
      @kleenexpresslaundrette2218 4 ปีที่แล้ว

      9:05

    • @christianalvarez5409
      @christianalvarez5409 4 ปีที่แล้ว +4

      @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.

  • @aifemremenekse1281
    @aifemremenekse1281 5 ปีที่แล้ว +11

    I cannot express my feelings man, u re perfect, greetings from METU 🇹🇷🇹🇷🇹🇷

  • @thechaching43
    @thechaching43 15 ปีที่แล้ว +8

    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!!

  • @nextblain
    @nextblain 12 ปีที่แล้ว +3

    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.

  • @musaaddi
    @musaaddi 15 ปีที่แล้ว +2

    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.

  • @AndrewLitton
    @AndrewLitton 16 ปีที่แล้ว +7

    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

  • @skr5064
    @skr5064 16 ปีที่แล้ว +2

    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!

  • @PrinceFX
    @PrinceFX 15 ปีที่แล้ว +11

    Sal for teacher of the Decade/Century!!!!

  • @myXdarkXworld
    @myXdarkXworld 7 ปีที่แล้ว +2

    THANK YOU VERY MUCH , your work really helps me in my university and the way you explain D.E is just so great

  • @pedromonteiro8792
    @pedromonteiro8792 3 ปีที่แล้ว

    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 👊🏻

  • @thedanzjl
    @thedanzjl 6 ปีที่แล้ว +1

    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

  • @shapular
    @shapular 14 ปีที่แล้ว +1

    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.

  • @curtpiazza1688
    @curtpiazza1688 ปีที่แล้ว

    It's starting to sink in! 😮😊

  • @austinfox4130
    @austinfox4130 7 ปีที่แล้ว +6

    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.

    • @starliaghtsz8400
      @starliaghtsz8400 2 ปีที่แล้ว +1

      bruh just multiply everything with dx

    • @CH-yp3km
      @CH-yp3km ปีที่แล้ว

      @@starliaghtsz8400 unironically thank you lmao

    • @starliaghtsz8400
      @starliaghtsz8400 ปีที่แล้ว

      @@CH-yp3km lol its ok

  • @somebody5498
    @somebody5498 9 ปีที่แล้ว +7

    god bless you .you are the best.

  • @weraponpat1913
    @weraponpat1913 8 ปีที่แล้ว +20

    fuk it's very hard for me
    error 404 brain not found.

  • @FarFromEquilibrium
    @FarFromEquilibrium 16 ปีที่แล้ว +1

    this is not easy for me to get a grip on but Im appreciating the pedagogical finesse.

  • @OwinoOchieng-v2y
    @OwinoOchieng-v2y ปีที่แล้ว +1

    Thanks alot

  • @thefishgallery168
    @thefishgallery168 13 ปีที่แล้ว

    waah tnx for posting instructional videos of D.E ... it helps lots!!!!!!!!!!!!

  • @Ganjin88
    @Ganjin88 15 ปีที่แล้ว

    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.

  • @mohitsanjaymahajan3246
    @mohitsanjaymahajan3246 3 ปีที่แล้ว +1

    great man...

  • @coolio2654
    @coolio2654 8 ปีที่แล้ว

    Great video for seeing an example from Boyce's Differential Eq.s book explained more fully ;).

  • @Ahfjo
    @Ahfjo 12 ปีที่แล้ว

    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.

  • @leolson3
    @leolson3 11 ปีที่แล้ว

    Totally illuminating DE's for me. Thanks!

  • @m2moun1
    @m2moun1 13 ปีที่แล้ว +1

    khan is legend

  • @bhargavsagabala4810
    @bhargavsagabala4810 4 ปีที่แล้ว

    very satisfying explanation

  • @gdullard
    @gdullard 13 ปีที่แล้ว

    great teacher, better comedian haha 3:09

  • @Marinecorps1812
    @Marinecorps1812 13 ปีที่แล้ว

    @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

  • @angelscott9717
    @angelscott9717 6 ปีที่แล้ว

    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?

    • @mse312
      @mse312 6 ปีที่แล้ว

      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

  • @totasalam7060
    @totasalam7060 10 ปีที่แล้ว

    love it .. thank you very much

  • @UniverselGamer
    @UniverselGamer 13 ปีที่แล้ว

    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)?

  • @jeegaravaiya304
    @jeegaravaiya304 5 ปีที่แล้ว

    Why didn't you add x^2 * e^y y' to the Nx at 2:45. Isn't y a function of x??

  • @HEL1Z
    @HEL1Z 12 ปีที่แล้ว

    i got it in the next video, thnx

  • @sircharles9715
    @sircharles9715 7 ปีที่แล้ว

    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.

  • @NitishChauhan1
    @NitishChauhan1 11 ปีที่แล้ว +26

    *MISTAKE*. At 8:50, f-prime of y is equal to -1 not +1

    • @litlemidgetful
      @litlemidgetful 10 ปีที่แล้ว +34

      he corrects it 2 minutes later

  • @tam3ree
    @tam3ree 13 ปีที่แล้ว

    Hey Sal, shouldn't you put "+C" at the end of psi at 6:40 ? Or is it included in f(y) ? Thank you!

  • @jammyjellyfish6612
    @jammyjellyfish6612 4 ปีที่แล้ว

    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?

  • @mohitsanjaymahajan3246
    @mohitsanjaymahajan3246 3 ปีที่แล้ว

    this are event helpfull now, 13 years later from the day they were created

  • @matt3DRC
    @matt3DRC 14 ปีที่แล้ว

    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
    @Amin_3k 6 ปีที่แล้ว +3

    If i somehow manage to pass this test, it is going to be a miracle. I don't understand ANYTHING :(

    • @nocturnalvisionmusic
      @nocturnalvisionmusic 2 ปีที่แล้ว

      Three years later but I hope you passed :)

    • @Amin_3k
      @Amin_3k 2 ปีที่แล้ว +2

      @@nocturnalvisionmusic Well... i dropped out 😂😂 Im in med school now. Couldnt take the math in Chemistry 😂

    • @nocturnalvisionmusic
      @nocturnalvisionmusic 2 ปีที่แล้ว

      @@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
      @Amin_3k 2 ปีที่แล้ว +1

      @@nocturnalvisionmusic Thank you my friend. Did you get your chemistry degree in the end?

    • @nocturnalvisionmusic
      @nocturnalvisionmusic 2 ปีที่แล้ว

      @@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) 😇

  • @ahmedjodeh268
    @ahmedjodeh268 5 ปีที่แล้ว

    Thank you bro

  • @VinothKumar-qo7ry
    @VinothKumar-qo7ry 7 ปีที่แล้ว

    Tanx lott sir!!

  • @paturelrebecca6763
    @paturelrebecca6763 8 ปีที่แล้ว +2

    where did the mines one go at 8:55 ?

    • @ninatsvetkova
      @ninatsvetkova 8 ปีที่แล้ว

      He corrects himself later in the video.

  • @mrlambochannel
    @mrlambochannel 12 ปีที่แล้ว

    u're the man!

  • @marymuthoni9668
    @marymuthoni9668 3 ปีที่แล้ว

    Good tutoring

  • @muhammadomarfarooq394
    @muhammadomarfarooq394 7 ปีที่แล้ว

    Awesome video>>>>

  • @manny34711
    @manny34711 13 ปีที่แล้ว +1

    shouldnt f'(y)=-1 instead of 1?

  • @mehanna84
    @mehanna84 16 ปีที่แล้ว

    thanks

  • @therealjordiano
    @therealjordiano 12 ปีที่แล้ว +1

    so coool

  • @rosesndwoos
    @rosesndwoos 5 ปีที่แล้ว

    Hello, is there a way to check if your function for c is correct?

  • @k88n
    @k88n 13 ปีที่แล้ว

    @Pastafarealist thanks for clearing that up.

  • @tjaistt
    @tjaistt 14 ปีที่แล้ว

    For partial of M ... why is cosx and 2x taken as constants? dont we have to differentiate cosx to -sinx?

  • @firaskurdistani3969
    @firaskurdistani3969 4 ปีที่แล้ว +1

    12 years ago😱😱

  • @mase_chiladin6706
    @mase_chiladin6706 8 ปีที่แล้ว +20

    Did you miss a negative sign for the f'(y)= 1 shouldnt it be = -1

    • @poorman4009
      @poorman4009 7 ปีที่แล้ว +5

      He corrected it in 9:40

  • @francisvergelvertudazo152
    @francisvergelvertudazo152 5 ปีที่แล้ว +2

    isn't that -y?

  • @Andrei-ds8qv
    @Andrei-ds8qv 8 ปีที่แล้ว

    thanks!

  • @reyboy4284
    @reyboy4284 7 ปีที่แล้ว

    So is this "zie" the same as finding the general solution?

  • @farrahsharif
    @farrahsharif 15 ปีที่แล้ว

    how do you check continuity? please reply

  • @arifahsraf1953
    @arifahsraf1953 8 ปีที่แล้ว

    very nice

  • @heromiIes
    @heromiIes 12 ปีที่แล้ว

    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.

  • @jdrabble1
    @jdrabble1 8 ปีที่แล้ว

    These are good, but I think it's time to update your DE sequence...

  • @mrknowmyself
    @mrknowmyself 6 ปีที่แล้ว

    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?

  • @shujaa_X
    @shujaa_X 4 ปีที่แล้ว

    I am from LGU

  • @mkvazowski
    @mkvazowski 2 ปีที่แล้ว +2

    f'(y)=-1 not 1 ?!?!?!
    Sorry

  • @sanjaysrinivaas649
    @sanjaysrinivaas649 8 ปีที่แล้ว

    how is derivative of psi wrt x =0 (video 3:30)pls answer!

    • @rnomadrs
      @rnomadrs 8 ปีที่แล้ว

      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.

    • @thehomiebearfifa3528
      @thehomiebearfifa3528 8 ปีที่แล้ว +1

      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

    • @rnomadrs
      @rnomadrs 8 ปีที่แล้ว

      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.

  • @samirajodeir1285
    @samirajodeir1285 11 หลายเดือนก่อน

    My and Nx are not equal!! My has +1Xe^y but Nx has +2Xe^y

  • @Leonitusworm
    @Leonitusworm 13 ปีที่แล้ว

    at 7:00 shouldnt the derivative for the f(y) be f '(y)(dy/dx)?

  • @TheMamed
    @TheMamed 9 ปีที่แล้ว +39

    i cant read anything on this quality >_

    • @mubeenshahid786
      @mubeenshahid786 7 ปีที่แล้ว +7

      I can perfectly understand on my macbook air which even has a low resolution

    • @zayedacademy988
      @zayedacademy988 7 ปีที่แล้ว

      watch our videos ,we are recreating his videos in a great way

    • @valkarez1137
      @valkarez1137 5 ปีที่แล้ว +1

      arent you in highschool? how are your eyes so bad lol

  • @salymamani2794
    @salymamani2794 7 ปีที่แล้ว

    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.

  • @budman533
    @budman533 14 ปีที่แล้ว

    LOL @ 3:00 , priceless

  • @andrizzyv1817
    @andrizzyv1817 2 ปีที่แล้ว

    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.

  • @793Rich
    @793Rich 10 ปีที่แล้ว +20

    My wife???

    • @BeamishBloom
      @BeamishBloom 10 ปีที่แล้ว +7

      yes i think hes married.

  • @bbltp49
    @bbltp49 11 ปีที่แล้ว

    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

  • @xoppa09
    @xoppa09 7 ปีที่แล้ว

    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?

    • @matheusiury6468
      @matheusiury6468 7 ปีที่แล้ว

      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 ^^

  • @anifowosevictorojoade8052
    @anifowosevictorojoade8052 6 ปีที่แล้ว

    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.

  • @ryuusel
    @ryuusel 15 ปีที่แล้ว

    Wait, didn't see that you corrected it.
    I should start watching the whole video before asking questions.

  • @fermixx
    @fermixx 15 ปีที่แล้ว

    its me the only one who gets lost with so many derivatives, anti derivatives, psi's, x's, y's ?

  • @mosesmccabe8983
    @mosesmccabe8983 9 ปีที่แล้ว

    wait, how is Mx = Nx? when Mx = (cosx + xe^y) and Ny = (cosx + 2xe^y)

    • @erikphillips1179
      @erikphillips1179 9 ปีที่แล้ว +1

      moses mccabe My = Nx. If he said otherwise, it was a simple slip up.

  • @mauroprovatos
    @mauroprovatos 15 ปีที่แล้ว

    but (sinx+x^2 * e^y) is multiplied by y', you didnt isolate it from y'. :/

  • @anzatzi
    @anzatzi 11 ปีที่แล้ว

    dont hate him--he just has a different take

  • @ryuusel
    @ryuusel 15 ปีที่แล้ว

    At ~8:50, wouldn't f'(y) = -1 instead of 1?

    • @shaktikashyap6
      @shaktikashyap6 3 ปีที่แล้ว

      Keep watching sal corrected it in the next step..

  • @suivzmoi
    @suivzmoi 14 ปีที่แล้ว

    hi are you canadian

  • @gonzoredux
    @gonzoredux 15 ปีที่แล้ว

    i thought there was a critter in my house for a second....ha!

  • @mjktrash
    @mjktrash 14 ปีที่แล้ว

    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...

  • @mr_wormhole
    @mr_wormhole 6 ปีที่แล้ว

    this video makes me puke on differential equations more.Thanks Khan Academy

  • @k88n
    @k88n 14 ปีที่แล้ว

    How is M and N exaxt if they differ with a ...1xe... = .... 2xe....
    That's not the same equations.

  • @z.r1999
    @z.r1999 3 ปีที่แล้ว

    what is ZII ...The answer proves what?

  • @gauravagarwal7508
    @gauravagarwal7508 10 ปีที่แล้ว

    Couldn't u intergral N with respect to y. Wouldn't that be easier

  • @AndrewEG
    @AndrewEG 10 ปีที่แล้ว +1

    240p video sucks. it used to be 480p... It's about as clear as soup youtube

    • @jefftee448
      @jefftee448 9 ปีที่แล้ว

      Andrew Gallagher Yea, I know! It should at least be 480

    • @zayedacademy988
      @zayedacademy988 7 ปีที่แล้ว

      watch our videos ,we are remaking old khan academy videos in a great way

  • @michyxmmx8987
    @michyxmmx8987 9 ปีที่แล้ว +3

    My brain D:

  • @denoke719
    @denoke719 9 หลายเดือนก่อน

    Who's watching in 2024😅

  • @EscanderBeats
    @EscanderBeats 2 ปีที่แล้ว

    😶14 years ago

  • @ikhebnietstedoen1
    @ikhebnietstedoen1 11 ปีที่แล้ว +2

    do Wronksi please

    • @ch0vits
      @ch0vits 10 ปีที่แล้ว

      ditto

  • @HEL1Z
    @HEL1Z 12 ปีที่แล้ว

    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

  • @tayyabuuu
    @tayyabuuu 14 ปีที่แล้ว

    there is a mistake in taking the differential of M !

  • @granyatee
    @granyatee 15 ปีที่แล้ว

    It is a two!... he says that xD
    it just looks like a 1...

  • @shmittythepirate
    @shmittythepirate 13 ปีที่แล้ว

    @manny34711 yeah...

  • @ZhangyXD
    @ZhangyXD 15 ปีที่แล้ว

    at 1:56 instead of 2x u wrote 1x
    opps lol