What is the most general method of approximating arbitrary systems of ODEs of 4 variables(x,y,z,t) that fit these conditions? The conditions that are assumed true of the ODEs are: 1) that I require differentials to be explicitly defined (but they can be defined in terms of other differentials). 2) that time is assumed linear (ei, it's a 3 variable system described in terms of 4, but the 4th is known) That is: dx=y^2+sin(x) dy=-dz+y*t dz=t*z would be valid, because dx,dy, and dz are explicitly defined and alone on one side. dx=f(dx) would be invalid, because I don't want to solve implicit equations. f(dx,x,y,z,t) = g(x,y,z,t) would be invalid, because I don't want to have to move all the junk to the other side to get an explicit definition of dx.