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A strange non-linear differential equation 

Maths 505
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Full solution development for this interesting non linear differential equation with expansion on a particular case relating the function y(x) to a constant of integration.
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3 окт 2024

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Комментарии : 20   
@barberickarc3460
@barberickarc3460 3 месяца назад
tried solving this one for myself and after finishing the first integration, getting stuck, and checking wolfram alpha I realised how in over my head I was
@CM63_France
@CM63_France 3 месяца назад
Hi, "terribly sorry about that" : 0:46 , 7:55 , 10:20 , "ok, cool" : 1:31 .
@Calcprof
@Calcprof 3 месяца назад
The sum can be expressed in terms of the Poly-logarithm, or if you like the Hurwitz zeta function.
@XclusiveScienceSecrets
@XclusiveScienceSecrets 3 месяца назад
Would you like to check our answers with a dilogarithm? My version: x+B=-y*ln|exp(y)/A-1|+ln|exp(y)-A|-Li_2(exp(y)/A) I used the reflection formula to simplify the argument of the dilogarithm.
@lakshay3745
@lakshay3745 3 месяца назад
I thought you were gonna write the final answer in terms of Di-logarithm
@holyshit922
@holyshit922 3 месяца назад
Yes , but this equation is second order reducible to first order with substitution y'=u(y) After reduction to first order we will get two equations and one of these equations is linear but problems may appear in integration
@xizar0rg
@xizar0rg 3 месяца назад
This seems kind of like it lost the thread somewhere, unless we're just glossing over that there's no closed form solution while being content that we found a range for it. Did I miss something?
@MrWael1970
@MrWael1970 3 месяца назад
Thank you for your fruitful effort.
@lih3391
@lih3391 3 месяца назад
Heres a horrendously scrambled equation which I hope is not too hard or easy: y'+log_[x^x](y^y)=(sinx/lnx)*y^(-lnx-1)
@Akshaylive
@Akshaylive 3 месяца назад
Most underrated channel on RU-vid.
@XclusiveScienceSecrets
@XclusiveScienceSecrets 3 месяца назад
Truly, all teachers of calculus should recommend their students to watch this channel. For their own benefit.
@satyam-isical
@satyam-isical 3 месяца назад
Since y=0 is the obvious solution & there's no obvious solution so it's only solution😂
@SnowboardAddict37
@SnowboardAddict37 3 месяца назад
Banger alert
@unknownplayer493
@unknownplayer493 3 месяца назад
it's an exact differential equation, so the solution is (y^3)/6 +Ay +ln(sqrt(c-2y)) = x + C
@tyyt-dp2rf
@tyyt-dp2rf 3 месяца назад
Im huge fan of "dearavly sorry sorry about that" *Typu mg horribly drung
@MRGamesStreamer
@MRGamesStreamer 3 месяца назад
Nice also put videos for matrices
@Anonymous-Indian..2003
@Anonymous-Indian..2003 3 месяца назад
Hi bro 👋
@maths_505
@maths_505 3 месяца назад
Sup bro
@redroach401
@redroach401 3 месяца назад
@@maths_505 Soup bro
@felipefred1279
@felipefred1279 3 месяца назад
I didn’t like the answer, but yeah nice problem 😅
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