The question did not state to assume that it mixes perfectly. Isn't that a problem? (I ask because in my differential equations module they always state "which mixes perfectly...")
@@j3s0n I bet diffusion of substances into other substances has been modelled before, but I also bet that the equation would be far more complex. Far beyond the scope of what the goal of the video was, no doubt.
I just got a 98 on my differential exam and I owe It to this wonderful man because he taught me reduction of orders and variation of parameters, and I studied of course. Thank you very much.
@@MrPanzerTanzer This is the real tragedy. If you're not flexible in units, all the really great work of the early 20th century won't make sense to you.
I loved it. The contents of the first 4 minutes deserved to take longer and be slowly explained because that's the most crucial and difficult part in my opinion.
I have this question in my textbook and was stuck at it since the past couple of days. I was about to go to my teacher to clear this doubt but then magically youtube recommends me your video. It's like you can read minds.
To sidestep the well known fact that the density (mass per unit volume) of alcohol diluted in water varies with concentration, you could specify "by mass" instead of "by volume."
_Separable_ differential equations are important for science or engineering majors. Most (all?) differential equations that describe the natural world are "autonomous" differential equations, which are always separable. This is essentially a consequence of one of the fundamental assumptions in the philosophy of science - that natural laws are constants of the universe, they don't independently change with respect to time.
Hi @blackpenredpen I know this is an old video, but I wanted to let you know that I struggle with connecting the maths to word problems. Therefore, this video is very helpful to me and I really hope that you will make more in the future! Thank you for you contribution on YT :)
Woah, first time I see a differential equation solved like that lmao, usually my teachers say "assume the answer is in the form X(t)=Ke^(-t/tau)+C (by the way I had a calculus class, we NEVER learned how to solve a differential equation..) And it's actually simple !
3:46 wait, if the question uses percentage for the concentration of flow rate in, shouldn't we also use percentage for the concentration of flow rate out? EDIT: nvm if i tried to multiply it by 100% it will give the same thing lol Note to self: 5:49 Got it from using u substitution for the denominator 6:03 +C on the left hand side is "moved" to the right hand side, making it C-C, making it just C1 (since we don't actually know what C is)
my light's were off and I was watching this vid alone with headphones in my room and my piano 3 meters behind me. I almost shit myself after hearing the piano melody at the end of the vid. Thanks.
Can we do a part 2 and learn some fluid dynamics? I really want to know how the concentration of alcohol behaves as a function of time and space. This is probably more in Dr. Peyam's domain though.
lets say they were pumped out at diff rates, if we wanted the amt of liquid total for a specific time, we would just have delta(r) or rin - rout, r = rate. so Vol(0) + delta(r)*time = vol(time). but why do they always seem to make it the same rate for these problems? doesnt seem that tough to calc the extra bit.
I personally find treating it as a linear DE and using an integrating factor easier than a separable DE. I also find it easier to plug in the initial value conditions while the equation is still implicit to avoid having to change the constant at every step. Is there any particular reason why you did it your way? Or is that just your preference?
Could you derive the Navier-Stokes equation in cylindrical coordinates without the use of the gradient operator ? For example, using differential elements; I think is a great example of how cylindrical coordinates work, subject even avoided by most fluid mechanics textbooks.
How do you set up the equation if the rate in and the rate out are different? I have a problem where the rate in is 5L/min and the rate out is 3L/min with an initial volume of 100L. I don't know how to set up the concentration out
@@blackpenredpen Haha. This reminds me of my conversation with one of my students. We went over a problem that said something like at the beach, the wave is traveling away from the shore at a certain velocity. My student was like, 'I surf a lot, and, not one time in my life, that I see a wave traveling away from the shore'. I was like, hmmm, true that, but, I guess, we don't care lol. As a mathematician, we don't really put the problem in the perspective of the real world haha.
Hi @blackpenredpen! Every time you do this operation (7:44) I make the same question to myself! WHY +-C1 is just another constant? We lose one solution of the equation! By the way I asked the same question in your website several months ago... www.blackpenredpen.com/discussions/math-problems/merging-constants-when-solving-diff-equations
Marc Darné Marí hi Marc. Because the constant is to be found later on anyway. We are just relabeling the constant. In here, my constant C=-15 If you use -C, then your C would be 15. But once we put it back to the eq, we will have the same eq. And that’s what it matters.
@@blackpenredpen Many Thanks! So according to that, if we don't have initial conditions to compute the value of the constant, we MUST maintain the +- isn't it? Please, make a video of this! Just for fun...
![⭐️( ลอยกระทง 2024 ) Ver. แดนซ์ Remix BY [ ดีเจกิต รีมิกซ์ ]](http://i.ytimg.com/vi/rMWOLhgXUHc/mqdefault.jpg)
The question did not state to assume that it mixes perfectly. Isn't that a problem? (I ask because in my differential equations module they always state "which mixes perfectly...")
Yes, I should have included that.
@@blackpenredpen it's okay, I still love the video xD
I just pinned this comment so that people will see this detail!
I don't see how you could solve it though unless you assume the mix rate is constant
@@j3s0n I bet diffusion of substances into other substances has been modelled before, but I also bet that the equation would be far more complex. Far beyond the scope of what the goal of the video was, no doubt.
I just got a 98 on my differential exam and I owe It to this wonderful man because he taught me reduction of orders and variation of parameters, and I studied of course. Thank you very much.
That’s so awesome! And of course you put in the time and effort too!! Great job!
@@blackpenredpen Not good enough for in-and-out though...😏
@@huntertuohey9264😂
Galon/min
Cries in EU
Even tho it doesnt really matter for this problem
Not only in EU... in the entire world outside USA and Myanmar....
@@hassanalihusseini1717 i hate how we use gallon, inch, etc
Mixing beer. Cries in Germany.
@@MrPanzerTanzer This is the real tragedy. If you're not flexible in units, all the really great work of the early 20th century won't make sense to you.
@@ronaldjensen2948 If you're not flexible in your units of beer, you don't make sense to me.
I have never had differential equations before (just measure them with recursion summation) and this is a clear example. Yay
I loved it. The contents of the first 4 minutes deserved to take longer and be slowly explained because that's the most crucial and difficult part in my opinion.
I have this question in my textbook and was stuck at it since the past couple of days. I was about to go to my teacher to clear this doubt but then magically youtube recommends me your video.
It's like you can read minds.
I used to hate the constant... Now I am starting to love it!
This was a great explanation in showing it as a separable differential equation.
To sidestep the well known fact that the density (mass per unit volume) of alcohol diluted in water varies with concentration, you could specify "by mass" instead of "by volume."
"唯一“ melody at the end just makes this video another level
_Separable_ differential equations are important for science or engineering majors. Most (all?) differential equations that describe the natural world are "autonomous" differential equations, which are always separable.
This is essentially a consequence of one of the fundamental assumptions in the philosophy of science - that natural laws are constants of the universe, they don't independently change with respect to time.
Thank you so much! Now I understand this topic much better
Hi @blackpenredpen I know this is an old video, but I wanted to let you know that I struggle with connecting the maths to word problems. Therefore, this video is very helpful to me and I really hope that you will make more in the future! Thank you for you contribution on YT :)
You are the GOAT!!! Just in time for my differential equations test!
Cool video about derivates but also I just started precalculus and I'm studying optimization using first and second derivates
Thanks for this class it helped me to understand this question easier
at 6:00 i dont understand why you need to divide with 1/-0.01
Dude, thank you so much! I have a time conflict with my chem lab so I missed this lecture last week! Perfect timing!
The formula for alcohol (the drinkable kind) is C2H5OH. Well, for an organic chemist anyway.
Ethanol😀
Yay! Besides this video, I also like the worksheet problem 2 which involves Newton's Law of cooling on forensic!
Plz do a short overview of recursively defined sequences! :)
Nice explanation dude😉
10/10 better than my calc lecture on this
Woah, first time I see a differential equation solved like that lmao, usually my teachers say "assume the answer is in the form X(t)=Ke^(-t/tau)+C (by the way I had a calculus class, we NEVER learned how to solve a differential equation..)
And it's actually simple !
Tryphon, un ZOUAVE ??! They can get really damn hard
@@sherllymentalism4756 Of course, but this simple case comes up quite a lot so it's very useful to know how to solve that
Now can you do a video on partial differential equations please? I am struggling with this course.
Hon2fun
You can check out dr. Peyam! He is teaching a PDE course now and making videos along the way.
Excelent video! An interesting example of diferencial equation theory.
Greetings from Spain.
3:46 wait, if the question uses percentage for the concentration of flow rate in, shouldn't we also use percentage for the concentration of flow rate out?
EDIT: nvm if i tried to multiply it by 100% it will give the same thing lol
Note to self:
5:49 Got it from using u substitution for the denominator
6:03 +C on the left hand side is "moved" to the right hand side, making it C-C, making it just C1 (since we don't actually know what C is)
Epic explanation.
next time you should do a problem with different rates going in and out. this is great for learning the basic idea though
My dude, you are amazing! Thank you so much!
my light's were off and I was watching this vid alone with headphones in my room and my piano 3 meters behind me. I almost shit myself after hearing the piano melody at the end of the vid. Thanks.
This man really be dual wielding markers
Ah! This is great! But this video came out the day after my exam which surprised me with this #yay
Great video!
How about cos(x)=x?
The size of a gallon depends on what you are measuring and where it is located. There is only one kind of litre :)
Easier to do it using characteristic polynomial and undetermined coefficients for rather than separation of variables.
Sir do you have videos of integration by algebraic substitution?
Cool video, learned a lot but the random fade-in piano at the end of the vid caused a brief spook for me since I'm watching this early in the morning.
thank you
Imagine it with a reaction, welcome into the chemical engineer life
Please do this question
Solve for x
x^sqrt(x) = 3x/2
c1 = 189.711998
Can we do a part 2 and learn some fluid dynamics? I really want to know how the concentration of alcohol behaves as a function of time and space. This is probably more in Dr. Peyam's domain though.
Does it involve PDE?
@@blackpenredpen I think so. Or you could write a program to simulate the behavior.
Well stated! I need to have a beer after this!
what happen to the 4% alcohol (by volume)?
I am confused why in this question, you use variable separable and when I tried a similar question, it is said that I must use integrating factor.
Thanks for this. I tried to solve this problem scientifically and got really drunk
Me when the teacher says "let's add salt to this solution": yaaaaaaaawwwwwwwwn.
Me when were talkin about beer: Oh I get it now!
YOU DIDN'T SAY "THAT'S IT"!!
unsubbing
jk
lets say they were pumped out at diff rates, if we wanted the amt of liquid total for a specific time, we would just have delta(r) or rin - rout, r = rate. so Vol(0) + delta(r)*time = vol(time). but why do they always seem to make it the same rate for these problems? doesnt seem that tough to calc the extra bit.
I personally find treating it as a linear DE and using an integrating factor easier than a separable DE. I also find it easier to plug in the initial value conditions while the equation is still implicit to avoid having to change the constant at every step. Is there any particular reason why you did it your way? Or is that just your preference?
Hey blackpenredpen , where did you get your whiteboard from?
oh what i heard the outro and was wondering when did i play my music
At 5:50 why he divide by -0.01
how to solve the lim as x tends to infinity e^x/x^e 🤔
Could you derive the Navier-Stokes equation in cylindrical coordinates without the use of the gradient operator ? For example, using differential elements; I think is a great example of how cylindrical coordinates work, subject even avoided by most fluid mechanics textbooks.
I have a question for u. Can u prove that 1+3+6+10+....+n(n+1)/2=n(n+1)(2n+1)/6?
Sorry I mean =n(n+1)(n+2)/6
Do you have an example where the outflow is larger than the flow in?
I still don’t understand why rate out is based on 500 gallon
x^(x+1)+1=(x+1)^x
Solve for x.
I know the answer is 0,1,2, how do you solve that?
Hi, I have a question: does e^2 is irrational? And does rational^complex is not rational?
isnt it o.35t? because its in time
You could have done with rate of beer being pumped out at a different rate. It would have been more interesting 😊
pls proof the "standard deviation" formula
How do you set up the equation if the rate in and the rate out are different? I have a problem where the rate in is 5L/min and the rate out is 3L/min with an initial volume of 100L. I don't know how to set up the concentration out
Level of interest very high with this one. I wonder why?
ME WHO OVERCOMPLECATE THINGGS: average of 7% and 4% for the concentration and the asnwer is still approximately 5.35.
Why did you get rid of your old intro? Yay
There is a critical assumption that during the time interval listed the beers aren't mixing and what goes out is only the original weaker beer.
Can u integrate plz,
X^2/(1+X^5) dx
I get the math somewhere but no one is able to solve it!!! Plz can you try sir!!!!??
Please find sec(z) =1
Ayan Lol
0 works.
No it is not 1 it is 1/2 sec(z) =1/2
@@blackpenredpen bro cos z = e find z
@@ghostexe9041 ????
Great!
The hardest part was to find the out volume. Everything else is too easy.
You need to pump out 5 gallon of bear PER MINUTE??? Man, I don't think I can finish your 11 minute video.
n choose k lol how come?
@@blackpenredpen I can't count 1-10 after 2 bottles of beer, so....
n choose k
Ah I see! I thought you mean pump out 5 gal per min is too slow. So you got me thinking about it.
@@blackpenredpen Haha. This reminds me of my conversation with one of my students. We went over a problem that said something like at the beach, the wave is traveling away from the shore at a certain velocity. My student was like, 'I surf a lot, and, not one time in my life, that I see a wave traveling away from the shore'. I was like, hmmm, true that, but, I guess, we don't care lol.
As a mathematician, we don't really put the problem in the perspective of the real world haha.
n choose k yea exactly! In fact this is just a typical diff eq word problem and honestly I don’t know how realistic some of the numbers are sometimes.
Maths is just as good as beer
Why is +-c3 just taken as c4?
Because the only difference between c4 and c3 is the signs. |c4|=|c3| he called it c4 in order to get rid of +-. Hope this helps.
@@agabe_8989 Ohhh like thaaat...thanks for explaining
@@anurankargupta1220 ur welcome
greattt
Universal Studios, hahaha.
OK, I was about sleep, but how can I?
He pumped out a lot of beer per minute, so I guess you can at least enjoy that?
hii sir
plzzz reply
Byee
The percentage of alcohol after an hour is "go home Johnny, you're DRUNK."
cringe
someone drunk alot to get just a little bit of increase in that concentration lol
No alcohol for kids.
#WHOA
Hi @blackpenredpen! Every time you do this operation (7:44) I make the same question to myself! WHY +-C1 is just another constant? We lose one solution of the equation!
By the way I asked the same question in your website several months ago... www.blackpenredpen.com/discussions/math-problems/merging-constants-when-solving-diff-equations
Marc Darné Marí hi Marc. Because the constant is to be found later on anyway. We are just relabeling the constant. In here, my constant C=-15
If you use -C, then your C would be 15.
But once we put it back to the eq, we will have the same eq. And that’s what it matters.
@@blackpenredpen Many Thanks! So according to that, if we don't have initial conditions to compute the value of the constant, we MUST maintain the +- isn't it? Please, make a video of this! Just for fun...
Hli
Third
Why do you hold your mike in your hand . Get a mike that can attach to your shirt .
Gg
First
Why did you get rid of your old intro? Yay