Derivative as divisor gives division by zero during initialization in Dymola

Question

I build a model that includes a derivative of dy/dx=5, as shown in the following segment, but the model fails during initialization in Dymola, in another question, it has been answered. The reason is that at time=0, the values of der(x) and der(y) are both 0. So there would be an error of division by 0.

model HowToExpressDerivative "dy/dx=5, how to describe this equation in Modelica?"
  extends Modelica.Icons.Example;
  Real x, y;
equation 
  x = time ^ 2;
  der(y) / der(x) = 5;
end HowToExpressDerivative;

Here is the result in Dymola:

But when I try the same model in the Wolfram System Modeler and OpenModelica, the model works fine.
In the Wolfram System Modeler, it uses the equation of der(y)/der(x)=5 directly.

My questions are:

1. Why Would the same model fail in Dymola?
2. Does Dymola NOT have the ability to do automatic symbolic manipulation to transform this equation of der(y)/der(x)=5 into der(y)=5*der(x)?
3. Or the numerical solver in Dymola can't handle this kind of situation?

Answer 1

Dymola does currently not recognize that trivial simplification in that case (it is done in another case), not because it would be too complicated, but because Dymola uses a simple rule:

Division in the Modelica code are safe, other divisions are not considered safe.

Thus der(x)/der(y)=5 indicates that division by der(y) is safe (even though it clearly isn't), whereas solving that equation technically involves dividing by 1/der(y) which isn't deemed safe (as it didn't occur in the Modelica code).

Obviously the logic can be improved, but the simplest solution is to use the following rule: don't divide in your code unless it is safe to do so.

A benefit of following that rule is that it will be possible to check all the original equations and see that they are satisfied (up to numerical precision) - without triggering division by zero.

Answer 2

Update: In Dymola2023 the model compiles and runs correctly.

// Initial Section
  der(x) := 2.0*time;
  der(y) := 5.0*der(x);
// --------------------------------------------------------------------------
// Dynamics Section
  der(x) := 2.0*time;
  der(y) := 5.0*der(x);