# Fitting solution function of NDSolve with a curve

• Mathematica
Gold Member
The following solves an IVP, giving the output as the function f3[x]:

Code:
s3 = NDSolve[{(-z1[t]^(3/2) + (1 + z1[t]^2)^(3/4))/(
3 (-z1[t] + Sqrt[1 + z1[t]^2])) == z1[t] z1'[t], z1[0] == 0.0001},
z1, {t, 0, 30}

f3[x_] := z1[x] /. First[s3];
My question is, how do I curve fit f3[x] to the function ##at^b## over domain ##t\in[0,1]##? Looks like ##t^{0.6}## does a good job (by eye) but is there a better way?

Table[f3[x], {x, 0, 1, 0.01}];
FindFit[%, a x^b, {a, b}, x]