@ecterrab 

Thank you for this, but I wanted something a little bit different, if Maple can do that. I should also note, I should have written Phi(X), not just Phi -- it needs to be coordinate dependant. Yours will work great for known metric, but I am trying to do it with arbitray metrics, and thus want the index expressions explicitly, and how the original vs. conformal expressions are related. Example: 

I will attach a screenshot of my worksheet and re-upload and hopefully you will be able to access it. 

MyConformal.mw

So I guess my question is -- based on my worksheet/screenshot if you can see it this time -- can I take my equation (3) and apply the transformation g_[] = exp(2 Phi(X)) g_[] easily, without needing to input each index pair, and arrive at my equation (5)? 

Thank you! 

Yes you can solve it. 

Do you have a file with an attempt at it? I can help you with it. 

@segfault 

Can you post the metric you are trying to work with? I promise I wont scoop any ideas, I have far to many projects of my own to worry about. 

I am sorry if I am thinking about it too simply. 

If you have a metric that you want to use, why not just manually enter it at the start and use the Setup command? Instead of initializing a metric then trying to change it? 

It would be easiest if we could see what you have attempted. Can you upload your worksheet? 

@segfault 

In the help page search  Physics,d_ or on your worksheet just do ?Physics,d_ 

Here is the link to the online version Physics,d_

@ecterrab 

Thank you for the response. Some of those commands I was aware of but some are new to me, I will use them in the future! 

Can you upload a worksheet with attempted solution? 

To @acer and @mmcdara

I am sorry for my very late response. I posted this question and then I had to step away from the problem for a while and now I am back into it. 

Thank you both for the replies, I was unaware that I could get it to run that quickly, must not have been thinking hard enough. Both of your responses make sense, but if something else comes up I will be sure to ask. 

Thank you again. 

@Scot Gould 

..

@dharr 

Thank you. Yes something like that but I don't think it fully solves my problem. I will reformulate. 

However, you are correct E2 is a mess, and that is a construct of how I want to solve the problem. I can elaborate in more detail and that might make it more clear what I was hoping for, I will edit my question afterwords. The differential equation I want to solve is: 

Sum((-1)^n*n*2^(n - 1)*a[n]*diff(Phi(r), r)^(-1 + 2*n), n = 1 .. N)=Q/r

I want the solution for Phi(r) to be of the form

diff(Phi(r), r) = Sum(b[i]/r^i, i = 1 .. infinity)

Now say I truncate the first sum to N=2 and I want to get the first few coefficients b[i] which solve this equation, obviously this is an infinite sum but if we consider just the first few terms for simplicity

We have that b[1]=-Q,b[2]=0,b[3]=4a[2]Q^3 so on and so on. Is there a command that can do this while considering what the previous found coefficients are (ie set b[1]=Q,b[2]=0)? 

For some reason it doesn't like using f[4](0). If you change to f[4] it works fine for me. 

@Paras31 

I will continue to look at this. 

@Paras31 

I can plot yes. If those are the plots you are looking for let me dive a little deeper into it and get back to you ASAP. 

@Paras31

Try this one:

dsolve_fix_2.mw