How can a system of non-linear differential equations be solved using Mathematica? More specifically, I understand the process that needs to be executed, but I don't understand how to make it work syntactically. The process as I understand it: Four expressions are given in four unknowns. Let the unknowns be expressed as x[n]. Each expression has three or less constant terms, which I'll just express as a[n]. These expressions are determined from an ideal, physical system which is being considered, so the constants can all be manipulated through experiment. dx/dt == ax - ax - ax == 0 dx/dt == ax/(a - x) - ax == 0 dx/dt == ax/(a - x) - ax == 0 x/a == (x/a)^n/(1+(x/a)^n To make the situation simpler, the top three differential expressions are set equal to zero to indicate a steady state process, so now I'm interested in what constitutes steady state conditions. In particular, I would like to get an expression in the form f(x) = g(x), where f(x) is simply x. Then, I can plot both f and g on a graph and find their points of intersection. My problem is that this is a burdensome calculation and I have no idea how to set a system like this up to be solved in the way described. I've looked up several function definitions on Wolfram help forums, including solve, eliminate, reduce and a few others, but none of the calculations simplified anything. Is there an alternative method?