Question: Creating surfaces composed of solutions to ODEs as parameters vary


I have an ODE with 3 parameters
diff(B[1](t), t) = piecewise(t < 1000, kaC*(R-B[1](t))-k[d1]*B[1](t), 1000 < t, -k[d1]*B[1](t))

I'd like to make a graph that shows how its solution vary as Kac and Kd vary. This could have an axis of the form:

            | /k[d]
  B(t)  |/_ __

which could contain a surface composed of the solutions as k[d] varies. Then a series of surfaces could be put together on the same axis to show what happens as kaC varies.

Some typical values are:

kaC = 6*10^(-2),
k[d1] = 7*10^(-3),
R = 1

I'd like to graph everything  in two orders of magnitude of these values for KaC and k[d1].

Currently I think the key obstacle is making a surface of solutions to the ODE; as once I can do that I think making a sequence of them on the same axis should be quite simple with Display




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