❖ Bernoulli Equation for Differential Equations , Part 1 ❖

In this video, I show how that by using a change of variable it is possible to make some equations into linear differential equations which we can then solve using an integrating factor.
This video show WHY this process works; if you are looking for a concrete example, check out the next part.
In the second video I solve a Bernoulli Equation by going through the complete process.
This video would be suitable for a student learning differential equations and who wanted to see the full derivation and why it works.

[csandreas]

i recently received my graade on differential equations and i got 45/45 thanks to Patrick!! <3

[TheUberPeople]

i have a test on this tomorrow, great timing!

[cierramunguia]

I'm glad you decided to do a derivation video and a example problems video!

[MuksEmmaN]

"If you want to see examples of me flying through this stuff".

When I grow up I want to have this much confidence :)

[marcos]

I see you have no regards for your own safety by using a permanent marker to do math. = Thug Life!

[theultimatereductionist]

Since learning about the Bernoulli differential equation in the 1980s,
I find it's so subtle & amazing & deep why we can solve y'=A(t)*y+B(t)*y^n for any (complex) number n,
but not y'=A(t)+B(t)*y^n when n is not 0, 1 or 2 (n=3 is sometimes called the Abel equation).

[ReWolWerKillZ]

wow i just realised you've never posted this type of D.E. until now. Perfect timing. Differential Equations class just started for everyone in college right now.

[franpolyphemus]

You're a godsend and a lifesaver. Thank you so much for this!

[coleforbes]

Patrick, you have gotten me through calculus. Thanks a lot!

[michaelm]

Your videos are amazing and makes this so much more understandable than in class.

[Bayonettamachinekill]

It’s incredible how the first program created by Ada Lovelace was all done with Bernoulli equations. Thank you Ada and Charles for inventing the computer.

[steartfires]

Brilliant explanation, thanks. That Leibniz was on another level.

[fredydeekrueger]

Damn, that sharpie gives me the chills. Great video either way!

[TheUberPeople]

You should cover the Ricatti equation too!

[Mathemusician]

I literally just had a test with Bernoulli equations yesterday.

[mmmchestnut]

odd that I started this really just this week

[alanwrigglesworth]

I was wondering if you could do a series on stochastic differential equation. can't find any good videos on it

[robertbrandywine]

Can you use a large whiteboard so that we can see more around what you are doing at one time?

[srinivasanbalan]

Hi Patrick, how will I solve the diff equation of the following format.
y'(t) = y + f(t) y^n + g(t). Your solution is highly appreciated.

[Docweed]

Correct me if I am wrong, you are right 98% of the derivation. The problem I see is there should be a negative in front of the a(t) value as the general form is dy/dt + p(t)y = q(t)y^n. Thus your proof would result in dy/dt = - p(t)y + q(t)y^n. Again please advise.