I have some problems solving a system in mathematica.
dX/dt = p * ( (S * X) / (S + k) ) - alfa * X dS/dt = alfa * ( S(i) - S) - (p / y)*((S * X) / (S + k) )
I have to write a linear aproximation for this system for S>>k ( S is much larger than k ) then to solve the aproximated system and use the solution for X and the data that I have in a table to obtain a numerical value for p. I have to plot the logarithm of X against the time, and estimate the slope.
How can I write a linear aproximation of a system in mathematica?
And then in my table I have several values for S, how can I retrive all values, then solve the equations for each value?