# Search results

1. ### Looking for a function with specific properties

Yes, that's sounds like what I was thinking of, and what I should have written! It's been a while since I had to use this terminology...
2. ### Looking for a function with specific properties

That's true oay, thanks! Maybe instead of "-It has an upper bound of 1" I should have written -it's limit at +-Infinity = 1 Not sure if even that makes it watertight. But anyway, HS-Scientist's suggestion is more suitable for what I need ;)
3. ### Looking for a function with specific properties

Thanks HS! Impressively quick response. That looks very promising actually. I might modify it with an extra parameter: f(x)=1-ce^(-(bx)^2) Then, by changing the value of b I can change the rate at which it approaches the upper bound. Anyway, looks very good and helpful! PS Sorry about using...
4. ### Looking for a function with specific properties

Hi everyone, I'm trying to find a function of single variable f(x) with the following properties: -It is symmetric around zero -It is differentiable everywhere -f'(x)≥0 for all x>0 -f'(x)=0 when x=0 -f'(x)≤0 for all x<0 (I think these last two actually follow from the first three?)...
5. ### Does the series k a^k have a name?

Thanks tiny-tim! I thought that might be the case. So many other series seem to have been named that I just thought it was odd! No, I can't prove the identity you gave in your post... yet! But I will try.
6. ### Does the series k a^k have a name?

Hi, a naive question here, but I was wondering if the series \sum^{∞}_{k=0} k a^{k} has a particular name? As in 'geometric series' for \sum^{∞}_{k=0} a^{k} ? And what about the more general \sum^{∞}_{k=0} k^{n} a^{k} ? As a related question, you seem to be able to get the formula for the...
7. ### Integrating directly from a pair of diff.eqs. without solving them

This is actually related to a post I made earlier in the differential equations forums, but I've since realized that solving the equations themselves is not necessarily the best way to get where I want to go. Perhaps it's better suited to this forum, since it is an integration problem that I...
8. ### Integrating 1/(x+ln(x))

Thanks again micromass. That solves my problem (or actually shows that it is unsolvable), and makes me appreciate Mathematica a bit more! Cheers, zeroseven
9. ### Integrating 1/(x+ln(x))

Thanks again, I always wondered how we could be sure that the integral of exp(-x^2) doesn't exist! So does this mean that when Mathematica works on an integral, it's actually running a rigorous mathematical proof on whether that integral exists or not? Does it use the Risch algorithm that you...
10. ### Integrating 1/(x+ln(x))

Thanks, that's helpful and very interesting. I have no idea how I would even begin to go about proving that a solution doesn't exist for an integral! Is this something that can only be done by computer algorithms?
11. ### Integrating 1/(x+ln(x))

I've been trying to figure out how to integrate 1/(x+ln(x)) but am not getting anywhere. Mathematica can't do it, and I haven't found it in lists of integrals. Does anyone know if this integral exists in closed form? Same goes for (x+ln(x))/(1+x+ln(x)) Thanks! zeroseven
12. ### Solving a pair of nonlinear coupled DEs

Another update: Lotka-Volterra equations was a great tip. They are almost identical in form to my equations, and cannot be solved with elementary functions, which convinces me that my equations can't be either. Lambert's W works in both cases, though. Anyone interested, have a look here...
13. ### Solving a pair of nonlinear coupled DEs

Interestingly (and frustratingly) I am unable to obtain the elementary function solution even for the special case a=b if I do it by eliminating dt. If I use the method I described in the first post, I can get a fairly simple elementary function for the integral that I need. But if I start by...
14. ### Solving a pair of nonlinear coupled DEs

First, thanks for the replies everyone! Second, I need to apologize.. Seems I made a small type in my first post ... the equations should be dx/dt=-ax-cxy dy/dt=-by-cxy (so bx in the first post should be by) I'm embarrassed about this happening in my very first post on the forums...
15. ### Solving a pair of nonlinear coupled DEs

Just wanted to add a bit more detail about what I need to do: The end result that I want is the integral \int^{∞}_{0}cx(t)y(t)dt So again, if it is possible to obtain this without having analytical solutions for x(t) and y(t) separately, that is fine. I don't even need x(t)y(t) like I...
16. ### Solving a pair of nonlinear coupled DEs

Hi everyone, new member zeroseven here. First, I want to say that it's great to have a forum like this! Looking forward to participating in the discussion. Anyway, I need to solve a pair of differential equations for an initial value problem, but am not sure if an analytical solution exists. I...