Applications of First Order Differential Equations - Mixing Concentrations 2

This video provides a lesson on how to model a mixture problem with different inflow and outflow rates using a linear first order differential equation.

[Mathispoweru]

Thank you for the message. There was one (300-t) that should have been 300+t. I annotated the correction. R2 should be 3/(300+t) because the amount of liquid in increasing by 1 gallon each minute since the inflow rate is higher than the outflow rate.

[ODogg]

When integrating after multiplying the integrating factor through the equation, you do not need the additional dt on the left-hand side of the equation... It is understood that the derivative with respect to t, (d/dt), is the portion of the equation being integrated.

[robertsonjoshua]

Thank you sir! You have no idea how much this helped!

[slamtoo]

i got the extra gallon added to the tank over time but why you replaced it with (t?)
Thank you.

[vvhead]

Thank You! This was very helpful for reviewing before an exam.

[AhmadNAlshammariKU]

I just wanna thank you because I understand the modeling of first order differential equations..
I will appreciate it to do some problems for economic or finance ... because they kinda different.. and I don't get it

thank you !!

[kimbryanduenas]

If you substitute infinity to t, you will also get infinity because of the +2t. I think the differential equation should have a cap of 600 lbs since the liquid pumped in has aconcentration of 2lbs/gal. At time equals infinity, the tank would have overflowed and the overflowing mixture will have a concentration of 2lbs/gal.

[SkOSn]

Thanks for the clear explanation. Subscribed and appreciation from Singapore :)

[josecohen]

I really enjoyed your video thanks! just one quick question if you get a chance,
right before you made an integrating factor couldnt you have just separated the equation? or is it was 8 + the rest of the right side it was non separable?

[danialdunson]

You need to make a playlist... your videos rarely come up on youtube recommended.

[AhmadNAlshammariKU]

Sir thanks for the video
but i think you had a mistake it should've been (3/300-t)
and thanks .. that was really helpful

[sebastianlopespereira]

im sorry around 7:40 you simplify your eqn, but im struggling to see how this is simplified.. to me it looks like a mistake .. but i could very well be wrong (Left hand side, 2nd line from the bottom) pls confirm

[MsLouloulepou]

Thank you so much. It was very well-explained :)

[neilrayno]

i dont understand why t (which is time) is added to 300 (which is a volume) 

[sebastianlopespereira]

i think d/dt should be replaced with (d/dt)+(3/(300+t))... again good chance i could be wrong