❖ Mixing Problems and Separable Differential Equations ❖

In this video, we explore mixing problems and how to solve them using first-order separable differential equations. Mixing problems are common in chemistry and other real-world scenarios where substances are added to and removed from a tank or container at certain rates.

We'll walk through a problem where a salt solution is added to a tank, thoroughly mixed, and drains out at the same rate. Using the concept of rate in minus rate out, we'll set up and solve a differential equation to determine how much salt is in the tank after 't' minutes. Along the way, we’ll cover:

Setting up the differential equation.
Solving for the amount of substance in the tank as a function of time.
Applying initial conditions to find particular solutions.
Interpreting real-world results from the mathematical model.
By the end of this video, you'll understand how to approach and solve mixing problems using differential equations, a powerful technique for modeling dynamic systems.

What You Will Learn:

How to set up a differential equation for mixing problems.
How to solve first-order separable differential equations.
How to apply initial conditions to find particular solutions.
Real-world applications of mixing problems in mathematics.
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#MixingProblems #DifferentialEquations #FirstOrderEquations #MathApplications #SeparableEquations #RateInRateOut #MathHelp #PatrickJMT

[Jyuni]

You are the main reason why i passed calculus 1, 2 and 3. Whenever i have a classmate that is struggling, i'd always tell them to watch your videos. Thank you so much, patrick!

[Macoranino]

10 years down the line and, your material is still relevant !

Great work, Patrick.

[rustyshivers]

I love that the main ad you have is "That Tutor Guy". I haven't even followed the link! For YEARS I have had great success with your videos. Nothing against the other guy. No One on the internet explains with the same clarity and consistency as you.
Thank you!

[neda]

May I say that you are AMAZING, omg finally I found someone that talks in my language. Professors usually skip a lot of steps assuming we know them!!! but your videos makes a lot of sense, that a lot, SUBSCRIBED 

[DangerDonkey]

I've always wanted to know why calculus textbooks always had this big hard-on for big tanks of brine. My textbook literally has a problem exactly like this... with brine. Anyways, you quite literally are the best math teacher on YouTube in my opinion. You're the reason I get by in engineering. If I could, I would donate. Keep being awesome.

[Dan-ykkd]

you and the khan academy guy should team up and be the kings of online education

[mikehenry]

I've been struggling with the modelling of equations exactly like the one you explained in your video for quite a while. All thanks to your amazing teaching ability, I can now do mixing problems flawlessly. Thanks Patrick!

[JoshStoller]

Thank you so much for filling in the gaps left by my Professor.

[jiadongyu]

Nearly 10 years on, this video is still really helpful. Thanks bro!

[MrKittenslayer]

I wish I had known about your tutorials sooner! So much easier to understand than my professor! Thanks a ton!

[williambarnett]

I just came across your channel and this section of differential equations has never been easy for me to understand until I watched this. THANK YOU

[nkad]

Your videos from 2010 are getting me grades in 2018. Can't thank you enough.

[patrickjmt]

@ermitz90 cause i am lazy and it is easier to write A instead of A(t).

it is the same reason people write: y = x - 3 instead of y(x) = x - 3

[blok]

this was extremely helpful! We learned this in Diff. Eq today and i left class thinking it was so tough. You made it so much simpler. I swear im spending the rest of the semester studying your videos! Thanks!!

[RGDynamics]

This made a hell of a lot more sense than my textbook, thanks for the crystal clear explanations.

[juniorjay]

Everybody kick in a few bucks to his Patreon, he deserves it more than most of our math professors!

[nicholasmartin]

Your explanation is very good. I'm only a sophomore in high school, and I understood you pretty well. Great video.

[OnTheBrink]

my professor completely blew through this stuff and my textbook is basically useless. Thanks for explaining it so clearly! you're a lifesaver =)

[williamvasiladiotis]

I know it’s been 8 years but thank you so much for this video! Much clearer than my ODE class

[ryantanner]

this video is awesome still 13 years later thank you!