Math help - Page 2

differentiating and then solving isn't really feasible imo. I think you're confusing this with differentiating, comparing the two derivatives and then finding a common initial point to prove that the two functions are equal.

Yeah ok I don't see a simple way of doing this without doing dE/dr = 0 (like you did already, and then trying to use the W function) to get:

(B/p)exp(-r/p) = (kq^2)/(r^2)

the way this Lambert function appears to work is for an equation of the form Y = Xexp(X), X = W(Y) where W is this Lambert function that is in mathematical programs.

so to get it in this form,

(r^2)exp(-r/p) = (pkq^2)/B taking the square root of both sides:
r.exp(-r/2p) = q.sqrt(pk/B) multiply by -1/2p
(-r/2p).exp(-r/2p) = -(q/2p).sqrt(pk/B)

now it is in the right for to use the Lambert function above (where X = -r/2p and Y = -(q/2p).sqrt(pk/B):

so -r/2p = W(-(q/2).sqrt(k/pB))
and r = -2p.W(-(q/2).sqrt(k/pB))

Unfortunately I don't think that helps you very much (but it was at least kinda interesting for me haha), but you do need to do this numerically I am pretty sure unless I am missing something quite fundamental (which is certainly possible), because this seems way to complicated and you can't really do much with it unless you have the constants because you need a numerical package to be honest to get the W function to work properly, it would be an arse to do yourself (you can even find the numerical calculation using Newton-Raphson on wikipedia). So yeah I don't see how you are supposed to find an analytical solution to this without using W because I certainly don't know how to do it and everywhere I looked on the net says that you have to do it with W because the solution isn't expressible as a combination of the basic operations (exponentials, polynomials, trig functions, logs etc)

Never heard of the Lambert function but it looks like Giga knows what he's talking about. I do agree that It's not possible to solve this kind of equation analytically using basic operations, so I'm not surprised that someone came up with this W function. The standard way of dealing with equations like this is to insert numerical values for the constants and then use some numerical method (Newton-Raphson, fix point iteration etc.)

Pretty sick problem.

Wow. I thought i was good at Maths in school. This shit is like wtf. I have absoultey NO idea what the hell everyones talking about in here. I feel pretty stupid. lol

I need a clear definition of what W is. need to get rid of any ambiguity in my answer

There must be something else they are looking for but I don't know what it is, sorry bro.

Is it multiple choice? Cuz if it is go with B, always works.