In Response To 'Re: Re: NDSolve'
I temporarily remove your goal of infinite accuracy in an approximate calculation and your other options. I'm just trying to simplify this to find and eliminate procedural errors first.
I also remove your request to solve for not only x and y but also y'. If we can get it to solve for x and y then we can later calculate y' from y.
What is left looks more like NDSolve examples in the help system.
It is a common mistake to try to use NDSolve with one or more variables that have not been assigned any value.
Imagine I ask you to to find EXACTLY the numerical solution to y'=q*y, but I refuse to tell you what value q has.
In your notebook it appears that n and m have no values. I believe that will guarantee NDSolve will fail.
After I assign arbitrary numbers to those I get an error about an inconsistent or redundant transcendental equation involving Log and E. Unfortunately I have not been able to pinpoint exactly which of your equations are responsible for that.
That problem needs to be found and fixed before anything more can be done.
Can you reproduce what I've seen and try to track down which of your exponentials is causing this?