A Differential Equation | The Result Will Surprise You!

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[@Lucky-rj8jd]

I just squared both sides and made differential equation into algebraic equations and applied Sri dharacharay formula and integrated at last. Resulting in a solution that looks rather complicated but is easy to derive. I don't like functions like lambert W because we have to relay on computers for the absolute answers and not our brain.😐

[@malte3756]

You have to rely on computers to get you values of the natural log or sin or a million other functions too

[@Lucky-rj8jd]

@@malte3756 I get what you are saying and I agree, I was just saying that if we can get the answer through just the brain work then why realy on computers. And please don't say that we can also derive logarithm on our on then why don't we do it, you know what I mean right?... whatever have a great night(it's night time in my country)

[@malte3756]

@@Lucky-rj8jd I get you, and finding a way around using the W function is neat still

[@basilelmasri7962]

How would that work then you would have the derivative squared is equal to X plus Y

[@Lucky-rj8jd]

@@basilelmasri7962 after squaring put y'= v {taking dy/dx = y'} After integrating You will get, y= vx +c Then substitute it into original equation we get, v²= vx +c +x Clearly it is a quadratic in v, let the roots be α,β Then v=α or v=β Substituting y' = v back we can easily solve the differential equation as it is a variable separable and get our final answer in terms of Explicit function, y= f(x) +c No need for lambert W function

[@manojsurya1005]

yeah same method , started with x+y = t²

[@user-ky5dy5hl4d]

It makes a difference when the constant C does not have to be +C. It can be -C and would give you a different answer.

[@bjorntorlarsson]

If we double u, we'll get to you! Happy birthday. That's what the evil math teacher would say. And that's actually the part of all of this that I myself might've come up with, after having learned from this channel since over a year. That's the kind of tricks I get. But if I ended up with that end solution (which I couldn't), I'd think it's not a solution but just an irrelevant reformulation.

[@mcwulf25]

Something so humble turns into a monster

[@ferretcatcher2377]

That’s the trouble with integration.

[@mathunt1130]

The thing which I would have done is write y(x)=xv(x), this would make it separable. This is a standard technique.

[@ThAlEdison]

Woo hoo, the solution you showed matched what I got. I did u=y'=sqrt(x+y), got a separable equation in just u and u', and solved from there.

[@montanasnack7483]

3:30 Had me crying

[@ssaamil]

Very nice one

[@SyberMath]

Thanks

[@arcturusgd]

You can do a double integral too √[x+y] dy dx = √[(x³+3x²y+3xy²+y³]/6

[@jamesstrickland833]

Why didn't you end up with two Lamberts like wolfram alpha?

[@Trimza42]

If you follow his answer at the end through, after solving for z namely squaring, you get the two Lambert W like Wolfram alpha gives. You then just undo the substitution z = x + y to get it in the same form.

[@del66404]

👏👏👏👏👏👏👏👏

[@broytingaravsol]

easy

[@KevinAPamwar]

Nice... You can also use the below substitution x + y = Z^2

[@surendrakverma555]

Good 👍

[@SyberMath]

Thanks

[@Yunglusss736]

5:01 Eminem over here

[@giuseppemalaguti435]

Posto u=x+y..risulta 2√(x+y)-2ln(1+√(x+y))=x+c.......isolare la y,non ne ho voglia

[@abdullahficici4298]

🏫

[@DonEnsley-yi2ql]

Before watching, temporary solution is y = (1+ W{-e^[-(x+c)/2]}) ² - x

[@stillprateekyet]

it is zed not zee

[@SyberMath]

Nooooo! Zeeeeee... 😁

[@paultoutounji3582]

Too much for me ..,.Must admit

[@mickodillon1480]

Strange result

[@bjorntorlarsson]

Helt muck liksom. Please never show this to any teacher of any kind!

[@basilelmasri7962]

Horrible video, too long, never solved for y but said earlier he would and he didn’t really separate by using a multi valued function

[@bjorntorlarsson]

But it was pretty exciting to try to follow. I am 2 disappointed. y?