The Elliptic Integral: A simple pendulum
When the angle of swing is not small, the motion of a pendulum is no longer well approximated by simple harmonic motion. The solution, by way of the elliptic integral, cannot be expressed in a finite number of terms of elementary functions.
However, a differential equation is a complete model of a problem. I think, this is what Newton was saying.
Writing the problem as finite differences, we can examine it numerically.... or pass it to a computer. Integration in time = Press play.