To gain some intuition on how we can use RNNs for time series, let us tailor the representation of the solution of a differential equation as a time series.
Consider the famous differential equation (Newton's equation of motion for damped harmonic oscillations, scaled in terms of dimensionless time)
$$ \frac{d^2x}{dt^2}+\eta\frac{dx}{dt}+x(t)=F(t), $$where \( \eta \) is a constant used in scaling time into a dimensionless variable and \( F(t) \) is an external force acting on the system. The constant \( \eta \) is a so-called damping.