Does a non-zero experiment startTime cause initial steady-state behavior in Modelica?

I am trying to understand the intended modeling behavior when using a non-zero StartTime parameter in the experiment annotation in Modelica. I would expect that it would simply suppress all output prior to StartTime, rather than affecting the behavior of the model. However, it appears that this is not the case. Consider this MWE:

model testStartTime

Real x;
Real y;
Real z;

initial equation
  x = 1;
  
equation
  der(x)=x;
  y = 200*time;
  z = exp(time);
  
   
annotation (
    experiment(StartTime = 3, StopTime = 8, Tolerance = 1e-06, Interval = 0.01));
end testStartTime;

I would expect x and z to match (to within numerical precision). That is, x(3.0) = z(3.0) = exp(3.0) ~= 20.08. What I actually get is z(3.0) = 20.08 (as expected), but x(3.0) = 1. Changing the initial value of x in the initial equation section causes x(3.0) to have this set initial value, without any system evolution over the interval 0 <= time < 3.0 taken into account. I see this same behavior using both Dymola 2023 and OpenModelica v1.23.1.

To me, this suggests that Modelica effectively imposes an additional set of steady-state equations (der(x)=0) during the [0, StartTime) interval, such that state variables retain their initial values at time=StartTime. Equations that are explicit in time (such as y and z in my example above) appear to work as expected-- the first output value of y is indeed 200*3.0 = 600.0, as expected by StartTime=3.0.

My question: is my assumption that Modelica imposes an implicit steady-state condition prior to the StartTime parameter correct? I cannot find a definition for this parameter in Sec 18.4 of the Modelica Specification (or anywhere else in the spec for that matter) and cannot understand the rationale for such behavior. I have several use-cases where suppressing all output prior to a prescribed StartTime is helpful, but I still need the system to evolve from initial conditions prior to that time. What is the StartTime parameter intended for?

Solution

This behaviour is the one I would expect: The integration starts at StartTime. It means that there is nothing happening before that time, because there simply is nothing.

The system of equation you are trying to solve is:

dx/dt = x

AND

x(StartTime) = 1

If my math is correct, the exact solution to this differential equation is:

x(t) = x(StartTime) * exp(t - StartTime) for t > StartTime

Changing the initial condition changes the solution: exp(t) is the solution of dx/dt=x AND x(0)=1.