A Differential Equation | The Result Will Surprise You!

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Опубликовано:

5 окт 2024

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Комментарии : 35

@Lucky-rj8jd 5 месяцев назад

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 4 месяца назад

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

@Lucky-rj8jd 4 месяца назад

@@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 4 месяца назад

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

@basilelmasri7962 4 месяца назад

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

@Lucky-rj8jd 4 месяца назад

@@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 5 месяцев назад

yeah same method , started with x+y = t²

@ThAlEdison 5 месяцев назад

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.

@mathunt1130 4 месяца назад

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

@bjorntorlarsson 4 месяца назад

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 5 месяцев назад

Something so humble turns into a monster

@ferretcatcher2377 4 месяца назад

That’s the trouble with integration.

@arcturusgd 4 месяца назад

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

@jamesstrickland833 5 месяцев назад

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

@Trimza42 5 месяцев назад

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.