Modeling the real world is hard. Physics often gives us differential equations, which are not so easy to solve, so what do we do? One option is to use a transfer function, which simplifies the differential equation into an algebraic one. Great. So now that we have something simpler, we can test different system inputs and measure the output in a simpler manner - no forward euler step simulations needed.
starting with different differential equations yields different transfer functions, the following script shows the step input (which sets the input to the differential equation to 1 at time zero) to the three simplest and most widely used transfer functions.