❖ Mixing Problems and Separable Differential Equations ❖

[@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!

[@ahmadsyed5221]

I like that

[@zedlepplin9450]

dude doing the same, from high school till college

[@stephendavis1837]

Same, and now hes the reason i'm gonna pass DifEQ too

[@janus2059]

@@stephendavis1837 Read your book and understand the example problems, then work problems from the book until you feel comfortable. That's how I got an A by teaching myself Diff EQs. I know you're probably done with the class now though.

[@Macoranino]

10 years down the line and, your material is still relevant ! Great work, Patrick.

[@MrNukenin16]

Calculus is 400 years old, and still relevant. His videos will likely be relevant for the next 500 years, assuming youtube remains for that long.

[@Macoranino]

@@MrNukenin16 hahaha makes a lot of sense.

[@rustyshivers7467]

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!

[@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 KZbin in my opinion. You're the reason I get by in engineering. If I could, I would donate. Keep being awesome.

[@neda2994]

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

[@mikehenry5]

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!

[@jiadongyu131]

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!

[@JoshStoller]

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

[@nkad378]

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

[@Dan-yk7kd]

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

[@CloroxBleach.]

professor leonard too ;)

[@briancruz3551]

don't forget professor dave, blackpenredpen and the organic chemistry tutor!

[@blok31092]

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!!

[@williambarnett3128]

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

[@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

[@OnTheBrink2113]

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

[@RGDynamics]

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

[@Superdoerr]

You're a great man! I've watched these vids all the way through calculus and now I am in diff eq on my way for a degree in physics. You're a huge help, thanks!

[@TashAngel17]

he makes it look so easy

[@the_martian_45]

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

[@konataGAMERZ]

Thanks for making these vids patrickJMT. Keep it up!

[@dude12125]

you are an amazing human being

[@williamvasiladiotis2903]

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

[@patrickjmt]

you are most welcome!

[@juniorjay001]

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

[@aaronvancuren7946]

Thank you for actually being a teacher unlike some of these theory professors that assume we can extrapolate from the book definitions lol.

[@ahmedbinhamad5407]

Can't imagine my math classes without u ! Thanks man

[@ryantanner1210]

this video is awesome still 13 years later thank you!

[@Gabriellaaaah]

If I pass this test tomorrow; I owe it all to you. Thank you for your time.

[@day500champ15]

I just came across these. So much easier to understand now.

[@kanefairweather4994]

This helped more than any other vid on the topic Thanks

[@tarunkumarjaiswal9918]

Thanks for explaining this in such a simple way . My DE exam is in 12 hrs and I'm confident now that I won't miss the tank problem 😆

[@MrSonyChaos]

Bless you mate. You're saving my studies

[@introversion8705]

thank you sir. your explanation is so helpful especially in online class. its funny how i didn't get this when my professor discuss but understand it well in your video. keep it up!

[@thecclan2]

My prof only taught us to solve the resulting diff eq using an integrating factor, so I've never thought to use separation. That's gonna save soooo much time haha. Thanks man

[@samali5374]

great job MR. AMAZING

[@SoumitraVadnerkar]

Sir, @05:25, it is clear that dA/dt=-A(t)/100; hence on integrating why doesn't the R.H.S. becomes (t^2)/200?

[@trinistylez2345]

you are the man!!!..best math teacher out there!!,,:D

[@payampajoohi166]

Yes! the videos from 2006 are still helpful

[@hellothereyoungsir]

You're my hero.

[@zzhaggerty359]

Could you do a problem where the volume of water in the tank changes?

[@TimeSum21]

Thanks, you have made mixing problems a lot clearer to me.

[@ThuNguyen-kw8im]

you saved my day and I'm sure for many people as well. Thank you for the videos, they are very helpful!

[@bballa99]

dude thanks i have a quiz tomorrow and this stuff might be on it!

[@AdonayZenebe]

Thanks for everything man. You've honestly helped make my life easier.

[@olietaylor]

at 6:43 how multiplying by dt and dividing by a(t) = 1/A(t) da ?? because multiplying by dt gives just "da" left on the left hand side and then surely dividing by A(t) would bring the left hand side to = "da/At" so why is the answer 1/a da??? please help

[@5566palo]

thanks a lot dude..i have an exam today..this will help me alot:))

[@theraagstar]

This video really helped me a lot!!! Thank you so much for this! You're such a blessing ❤

[@PolloJack]

Wonderfully worked out example. I have terrible handwriting so my notes are often useless and the book skipped several steps including the part where I messed up, multiplying by e.

[@bublgum123]

i love you and the way you teach hallelujah

[@reamabdulsalam524]

Thanks Patrick I was struggling substitute the initial condition but now I am ok many thanks please keep up can you also cover the complicated lakes problems please ? I could not understand them thanks

[@TK6917]

I do some exercises of mixing problem like this, but the solutions write the denominator of rate out with the variable t. When the rate out part should have variable t? sorry for my poor english.

[@shawnrusselld]

Your the best. Thanks for helping me understand.

[@XavierDeclined]

Thanks for this Patrick!

[@PrinceFreshXXXII]

Beautifully done

[@candybarbaran2629]

Thank You Patrick .. Your videos have been so helpful !

[@paoboonjinnz]

Why your C(out) is Mass/Volume of the tank? In my class, my professor told that the volume of the tank would change as a linear function. so your volume should not be constant.

[@alamachin]

thank you very much! I have my final exam on monday and this will certainly help

[@kookyjay]

Patrick, thanks for the fantastic explanation!

[@achen94]

what happened to your rate in (10L/min), it seems that you left that out, shouldn't it be dA/dt +A(t)/100= 10? Making this a first order linear diff eq instead of an easier separable equation?

[@zhoudanchen1021]

i think it's pretty clear cuz it's pure water flow in, water has no concentration, so when you multiply concentration it cancels out. watch video carefully, if it's salty water flow in, then that's the case you are talking about.

[@OsmanSaid93]

excuse me. Can u help me solve this problem? TQ - A tank with capacity limit of 1000 gallons initially contains 200 liter of pure water. Then at time t = 0, brine containing 5 lb of salt per gallon is allowed to enter the tank at a rate of 20 gal/min and the mixed solution is drained off at a rate of 10 gal/min. How much salt is in the tank at the point of overflowing? (it says that the tank INITIALLY contains pure water, and at the same time, at t = 0,they pump the salt) so what should I do? )

[@vn4228]

Great video with clear explanation. Thanks!

[@gipstar13]

I LOVE YOU! you are the reason why i'm passing!

[@kramer3214]

I know you get a lot of these praise comments but I just thought I'd shoot you another. I actually have a really good calc 2 professor (unlike most of these people) but hearing another person work these problems helps a lot. It especially helps when I'm studying for my final and my prof hasn't covered this stuff in a few months. So thanks :)

[@qwerty14142]

"It's a beautiful tank" I probably laughed harder than I should XD Thank you soooo much for the videos!

[@KaroFernanda]

Great explanation

[@TheClydeGamer]

I have some question involving some mixture problems but I don't get it much: How many pounds of 35% salt solution and how many pounds of 14% salt solution should be combined so that 50lb of a 20% salt solution are obtained? I tried to solve this using different equations but I'd come up with some negative answers...

[@MundusLitterae]

wow thanks!!! I have an exam today on this material and it really helped :D

[@Higgin96]

imagine if patrick was your professor... every class could be 10 minutes

[@patrickjmt]

never!

[@jacksonmadison9994]

You can also skip the separation of variables by using the characteristic polynomial. A’ + 1/100 * A = 0 R + 1/100 = Root = -1/100 Y = ce^(-1/100) c = A naught = 15 15e^(-1/100) If it weren’t homogenous you could also use undetermined coefficients to find y particular and add it to the homogenous solution.

[@nayramn]

thank you for always helping me.. hope to meet you in person..take care

[@RenegadeFury]

my friend you are amazing as always

[@smsexpress]

Great explanation, thanks

[@danieltrevino2289]

When I plug in your final answer in the calculator, the more time passes by the closer to 15 it gets, shouldn't it be the other way? The bigger the "t" the smaller the quantity of salt it should be? (15e^((-1/100)t)=A

[@SweetDreams49]

i love your vids! they help soooo much! THANKS :)

[@urecheurke2245]

What if the inlet stream had a certain concentration? Is that separable?

[@franciscadiente7072]

Patrick could you also do circuits. (differential equation RL and RC circuits)

[@grant3hanson]

Thanks, this helped a lot!

[@blueblur8420]

Thank you so much! You're so amazing!!!

[@liwenzeng4382]

Thanks it helps me a lot!

[@user-pf3vz3rd9h]

Hello Patrick, I'm looking for example problems for my 'computational methods for Engineers course' project and we're asked to use different methods to solve ODEs. Please help me find a problem I could work on

[@TheLovelaChannel]

bless you patrick

[@esmiileyyx6249]

what if it has two compartments? tank A and tank B?

[@ddisdain2276]

would you tell me if flow out is 5? how can i set up the ode? please answer me :) thanks you for good content.

[@Yun2ster]

If you were to differentiate ln(-1/100) + C (to check to see if your integration was correct), you would be get 0 since you are taking the derivative of a constant. The integral of (-1/100)dt is (-1/100)t + C and you can check by taking the derivative: -1/100 * t + C u=-1/100 v=t u prime= 0 v prime=1 u(v prime) + u prime(v) + 0 -1/100 * 1 +0*1 + 0 = -1/100

[@1hassan1100]

will you do a PDE. in the same way of example

[@Pratchaa]

what do you do iffthe problem involves two tanks? the problem i have says that a tankA has say 200 L of water with 40 g of salt in it and tankB has 200L of water with 20g of salt in it. tankA drains into tank B at a rate of 16L per minute. tank B drains out of as spout at a rate of 12L per minute and out of a different spout, 4 L per minute, which this one feeds back to tank A. tank A is also filled by a seperate spout with pure water at a rate of 12L per minute. how do i work that out??

[@therotaryrocket]

What if your A(0)=0? What if your initial condition states the amount of salt in the tank is 0? (pure water). How would I get the value of the C constant after integration? Thanks! Thanks for making this videos too! So very helpful. I even exponentiated each side to get rid of the ln[A], then I ended up with my new constant being 0, which cancels out the extremely important variable t. What to do?

[@opufy]

Damn that sure is one mighty fine tank there, bud.

[@drury2d8]

what if the tank does not have an outlet ? how will the equation change ?

[@nouraaliabuhlega4023]

Thank u so much Ppl i need help z there any 1 know a reference for deferential equations.! I neeed names

[@jeniney.6396]

Thanks so much! Awesome videos :)

[@r3vmixman]

Use the same idea, except this time, for Rate Out you have A(t) / (200 + 20t - 10t). Looks like your + C is zero since it says at t = 0 it is pure water. Where did you get this problem? I don't think it is separable.

[@Createch77]

nice, im doing diferential equations and it helped a lot. More videos pls :)

[@tominthetux]

Shouldn't the integral of -1/100 dt be ln(-1/100) + C?

[@JustEraseTheSystem]

this was really good thank you!

[@tonymwiti7755]

Awesome sir have enjoyed it

[@Pratchaa]

Into tankA: 12 L per minute pure water and 4L perminute water from tank B into tank B: 16 L per minute from tank A Out of tank A: 16 L per minute into tank B out of tank B: 4L per minute into tank A and 12L per minute drains out of the side

[@ermitz90]

May I know why you drop the t from A(t)??

[@Huda-dq9tm]

Thankyou so much.❤❤❤

[@hazimaznan2077]

very helpful. Thank you

[@aray-bibiserikbay3976]

good explanation, thank you! But can you expand your notes, I mean you write so much notes in little space