Bernoulli Differential Equations: Solution Methods and Exercises

[@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.

[@kingarvish4269]

wow :O smart boi

[@atrimandal4324]

Thank you for that second paragraph 🤔

[@ZweiZombies]

I can totally see this happening and fucking up an afternoon.. Thanks man!

[@angelmendez-rivera351]

He made a reference to the fact that he introduced a discontinuity later around minute 6 or so. Also, there is no real reason to make it explicit if the audience pays close attention to this. As for the integral, he has Ln|y(x)| = Integral(dx), which equivalent to |y(x)| = e^Integral(dx). If y(x) < 0, then -y(x) = Ce^x, which has y(x) = -Ce^x. However, C is a constant and it can absorb the negative sign if we let C = -D. In any case, your concern about the two integration constants is not important because the equation dy(x)/dx = y(x) has the well defined solution y = Ce^x for all x and all C. If C = 0, then y = 0, which is the trivial solution excluded by dividing by y. If not, then C can be whatever, and sign(C) determines sign(y(x)). So the solution only needs one constant in this instance.

[@kadusalgueirosa3290]

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 :)

[@lonamisa8377]

You could say i'm not a native english speaker

[@damiandassen7763]

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)?

[@jesusdavidrinconpuche2193]

Your explanations and your quality are improving every video. Congratulations

[@codemagenta2681]

Daumen hoch for the arbitrary constant e-Schlange.

[@BeattapeFactory]

hier machts mehr spass als in der vorlesung

[@guyparker3223]

Congrats on 20k subs !!

[@rayforever]

20k?

[@electromorphous]

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

[@Zzznmop]

I’m watching this while driving having a flammable day

[@Nithesh2002]

5:38 is a nice tongue twister

[@mujammilmanzoor7532]

You are great sirr.....well explained.....😊 Thank you.....your vedio is really helpful...

[@PapaFlammy69]

[@angeld3]

Excellent video papa ❤

[@elfaroukharb3979]

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

[@kacpertazbierski9355]

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

[@mipmip4575]

3:52 Euler ready for deployment

[@m322_yt]

E SCHLANGE

[@nawafaleid196]

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

[@anacarvalho7404]

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

[@vaibhavjakhar2001]

Well done... Great work

[@vaibhavjakhar2001]

U deserve it sir... Just be motivAted have a great day...

[@sayantaniguha8519]

Video starts at 2:56

[@mestanabdulxaliqli1369]

Thank you man :) You are awesome :D

[@aryansaxena4978]

Thanks man

[@PapaFlammy69]

:)

[@danex8000]

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!)

[@Koisheep]

danex8000 i think in that case you have to calculate the division and work from there -- it should reduce to a separable equation

[@karinano1stan]

oh baby this is so complicated

[@crazyjester993]

7:00 , 4:25 , 6:55

[@ThomasBiju]

Where do you film your videos?

[@boffo25]

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

[@Vexon51]

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

[@haris-spam6999]

at 2:31,focused out ,thanks me later for no reason .

[@helloitsme7553]

I would have picked harder examples tbh, those differential equations were just separable. Like if P(x)•Q(x)=0 it's always seperable

[@cristianmeraz4181]

thank you for shedding light on these bad boi's

[@michelebrun613]

Is it easible expandible to system of ODEs?

[@mohannadislaieh3009]

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

[@jonasdaverio9369]

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

[@krystalatchman347]

Link for video on solving types like Case 2?

[@wocannaseilai5983]

Very nice

[@Aleaxhs27]

you're awesome!!

[@carlosvargas2907]

Papa Euly at 3:52

[@BeattapeFactory]

an welcher uni studierst du? Das video kommt gerade gut fúr die prüfungen in paar wochen

[@safiullahmahar3536]

U r very energetic dear .help ful

[@PapaFlammy69]

[@muhammadalikashifkhan5556]

maths love buttons

[@moazahmed3280]

u r great .. keep fun

[@Nobody-Nowhere-Nothing]

This video has π amount of likes, nice

[@MoreCompute]

I L O V E T H I S V I D E O

[@atrimandal4324]

Oh Boi❤️🔥🔥🔥

[@سجىرعدرحيم]

خوش شرح يمكن الوحيده اني من العراق

[@nawafaleid196]

لا

[@pedronogarolli1004]

I was studying this yesterday. kek

[@Alexmar345]

Und der soll angeblich Lehrer werden. Niemals! Talent hoch 10

[@Alexmar345]

Flammable Maths ich verbiete es dir! 😔

[@jake_runs_the_world]

I just came

[@oscardavidalarcon2673]

More videos

[@FuhrerShattercore]

I'm gonna start saying e schlange. thanks

[@yarooborkowski5999]

So cool :)

[@harikishan5690]

nice!

[@kingarvish4269]

:D new video!!!! :D

[@cavver3523]

Good! :D

[@alexismiller2349]

Ninja's dead :c

[@jambaytshering312]

Huh... Makes me more angry

[@mipmip4575]

first

[@tanitoxeolee5767]

too fast not even understand what your saying,

[@kekeatibaua4906]

Tanito xeolee 😂😂😂

[@__krossell__]

Solve the following integral, it's interesting (x^2-1)/((x^2+1)(x^4+1)^(1/2))

[@giziemcbarns]

X^2