There is a long tradition that the first example in any computer language is a trivial program printing the string "Hello World". Since Modelica, the language used in System Modeler, is an equation-based language, printing a string does not make much sense. Instead our Hello World Modelica program solves a trivial differential equation:

The variable x in this equation is a dynamic variable (here also a state variable) that can change value over time. The time derivative is the derivative of x, represented as der(x) in Modelica. The following code is used to implement this model:

model HelloWorld "A differential equation"
  Real x(start=1);
equation
  der(x) = -x;
end HelloWorld;

The picture below shows the variable x in a ten second simulation:

For a step by step tutorial see Hello World.