Bernoulli Differential Equations: Solution Methods and Exercises

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Let us talk a bit about a special type of first order ordinary differential equations! :) It's not abstract this time, I swear! :D

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[PackSciences]

One point that is important and that isn't really mentioned:
At 2:55, you introduce a discontinuity without it being explicitly said.
In an isotropic field, the differential equations are often verified everywhere, and the fact that you have to "glue back" the two parts can sometimes be hard.
When you integrate at 10:12, you write only one constant C. Mathematically speaking, there are two constants so the solution has the form f(x) = x + C_1 on x < 0 and f(x) = x + C_2 on x > 0 and nothing guarantees that there are the same.
In physics, most of the time they will end up being the same "constants", but you should be careful, someday you'll encounter a problem in which the constant isn't the same.

[kadusalgueirosa]

sice I'm not an english native speaker and I have some problems with grammar, I'll make a simple sentence: I love u man, great video :)

[jesusdavidrinconpuche]

Your explanations and your quality are improving every video. Congratulations

[damiandassen]

I have maybe a fun idea for a video: how to calculate the inverse Laplace transform of a function. maybe inverse Laplace of ln(s)?

[BeattapeFactory]

hier machts mehr spass als in der vorlesung

[codemagenta]

Daumen hoch for the arbitrary constant e-Schlange.

[mujammilmanzoor]

You are great
Thank vedio is really helpful...

[Zzznmop]

I’m watching this while driving having a flammable day <3

[elfaroukharb]

yay, notifications working again. Cool video as usual :)

[electromorphous]

I'm the guy increasing you're views and likes.
Ps: you're a genius

[anacarvalho]

Good class, help me a lot!! Handsome teacher by the way

[danex]

Just already i am studying D.E. in my university, and i am learning the basics concepts. And seeing your playlist y can just understand a few topics of this theme. Thanks for your videos, you explain in a excellent way and i am so happy that i found this channel.
So, i know that you can do some change of variable to transform an D.E. and solve it more easy, but... in this case:
y' = (xy + 3x - y + 3)/(xy - 2x + 4y -8)
Or other case like:
y*y' = (2(y^4) + x^4)/(x(y^3))

How i know what changes i need to do so in the solution i can do it more easy? I tried to use the basic concepts i learn but i don't understand it, i'm so confusing and i always try to separate the variables, can you give me a little hint?
(Sorry for my english, i'm from Chile, have a happy day!)

[vaibhavjakhar]

Well done... Great work <3 keep it up.... success is not too far...!!!

[kacpertazbierski]

Flammy, play with some orthogonal basis derived from Sturm-Liouiville equations, i find it the sexiest thing understandable for ordinary humans :D

[nawafaleid]

Love your explaination - just a quick question, , , @7:20 shouldnt the left side have a negative value as well ? thanks :)

[boffo]

How about this function pow((s-1)/(s+1), s)/(pow(s, 2)-1). Can you find the inverse Laplace transform?

[Vexon]

Papino how long is the master's that you're going to do?

[jonasdaverio]

How could get rid of the absolute value in the ln|y| at the end?

[cristianmeraz]

thank you for shedding light on these bad boi's <# great refresher from my diff eq course and a great video as always

[mohannadislaieh]

Can u plz makee a vedio and explain the partiel derivatives?!