The fsolve command numerically solves for the variable. Since eqn1 has two variables, executing solset2(z) returns the statement, "Error, (in fsolve) z is in the equation, and is not solved for." On this example, you could replace fsolve with solve and, in the plot statement, get rid of the quote marks.

I appreciate the response, but how does this help? There is nothing wrong with my procedure, try2. Execute my code and then execute the following. > try2(1750., 0.3, 0.09, 96.48692660) You will get the response 1750., 0.3, 0.09, 96.48692660 [1.48692660, 13.3810029, 48.4459596, 33.982839, 15.354723, 15.681500, 6.699209] These are the correct residuals. The question remains, how do I get Maple to give me the best-fit if LSSolve won't pass the values to the procedure? Or, how can I get LSSolve to pass the values to the procedure? One more comment: This DE has an exact solution. We can get the best-fit using the following code: > data := [[0, 95], [11, 425], [22, 928], [33, 1358], [44, 1589], [56, 1683], [67, 1724]]; > try1 := proc (K, alpha, r, tm) local R; print(K, alpha, r, tm); # for debugging R := K/(1+alpha*exp(-r*(t-tm)))^(1/alpha); map ((d) -> eval(R, t = d[1])-d[2], data): end; > sol := Optimization[LSSolve](try1(K, alpha, r, tm), initialpoint = {r = 0.09, K = 1750, tm = 17, alpha = 0.3}); K, alpha, r, tm sol := [80.205987860140, [r = 0.0884814753475860612, alpha = 0.345995076771192566, tm = 17.9418639765759238, K = 1746.34336442594190]] Notice that, even though K, alpha, r, and tm are undefined, LSSolve still works! Why won't it work with dsolve?