Differential Equations - 11 - Modeling with 1st Order Diff. Eq's (Tank Problem)

Demonstrating how to model a system with a 1st order differential equation with a Tank Problem.

[harryr_]

i tried many tutorials and videos but non of them were clear as this... This series helped me alot ..

[milkcreightronny]

I appreciate you breaking everything down into simple terms i.e. dimensional analysis. Very easy to follow and comprehend.

[BillyBobby]

you are a gift from God, please know you are one of the reasons I am going to pass diff eq :)

[carterl]

I finally understand🙏🏻🙏🏻 Thank You. Hope both sides of ur pillow are cold when you go to sleep

[esraa]

what an amazing video!! thank you I understood all <33

[ProjectDuckHQ]

question: What happened to the (100+t)^2 s' when integrating? does that become 0? if so is it because of the integral of s'?

[kingbeauregard]

Just for fun, I decided to work this problem but without supplying any values until the last step, so I created some general formulas for the tank problem. A couple interesting results:

1) In the solution in the video, that term (t + 100)^2 in the bottom ... ? That squaring comes from the ratio "Out / (In - Out)", as in, the 2 gal/min and the 3 gal/min rates. You'd come up with some crazy exponents if those two rates weren't integers right next to each other, for example if it were 3 gal/min and 5 gal/min.

2) If the In and Out rates are the same, the solution changes such that it's a simple exponential curve that asymptotically approaches the point where the water in the tank is indistinguishable from the water coming in. The interesting thing is if you also assume a non-zero amount of salt initially in the tank: then the solution is the sum of the asymptotic result I just described, PLUS an exponential decay of the salt that was initially in the tank. That makes me want to use tiny discrete particles instead of salt, in two different colors, so I could watch the initial particles disappear while the new particles would gradually take over.

[rajinfootonchuriquen]

I use de UV method because yours too advance xd. Thants for your explanation.

[aidand.]

6:50, why are you taking the exponential to the integral of that? Is that Mew(t) and P(t)

[haiderimam]

what is mew and why do you multiply by equation

[aidand.]

how do we know it is rate coming in - rate coming out? Isn't rate of change final minus initial?

[neonlights]

What happened to 3 when you were integrating (100+t)^2 ?.

[rishitena]

how the exponential is integral the whole thing

[cooleren]

Umm how is the integral of 3(100+t)^2 is equal to (100+t)^3?? Thats not how the integral works, the answer should be 30000t+300t^2 +t^3 +C

[Carmen-uozi]

What happened to the 2 infront of (100+ t)s??

[kingbeauregard]

At first the final answer confused me: how could it be that the amount of salt is increasing at all times, and doesn't asymptotically approach a limit? Well the answer is, there is more water going into the tank than coming out, so that's where the increase comes from. If the deal were that 2 gallons were being pumped in and 2 gallons were being removed, then that changes the initial differential equation so that the volume is a constant "100" rather than "100 + t", which drastically alters the math, and indeed does give us the asymptotic behavior I was (mistakenly) expecting.

[olietaylor]

could you do an example where you explain why and what you’re doing please because the steps don’t make sense

[lillyzegarra]

You forget you're teaching DE to people that want to learn people that are trying very hard to understand the subject and when you start skipping steps you sabotage yourself and confuse everyone else. We are not stupid and we understand when the explanation is clear and obvious but it is almost as if you need to show off at a cost of confusing everyone else consequently you get all these angry comments which should be a hint to you that something is a miss and people watching this channel are dissatisfied with your tutoring. Do everyone a favor by not skipping steps it's stupid to tutor this way, do it right the first around and explain the logic behind the numbers. I'm so disappointed!