Why aren't all important differential equations solved and codified once and for all? This is not a number question, and I hope it is on topic.
I always wondered how come, with modern supercomputers, the most important DE, especially the ones that refer to Physics, haven't been patiently solved one by one, and codified for reference, the way a century ago they did with sines, trig values and log tables.
Do you have an answer and an explanation, if the answer is negative?

The Lorenz Attractor is a set of differential equations. It's also chaotic, in the sense that slight perturbations of the initial conditions rapidly diverge to different results.
A pre-calculated "solution" for it is thus meaningless, because a table could only contain finitely many values but you cannot usefully interpolate between them.
This also applies to many real-world fluid dynamics and gravitational systems: no analytic solutions available, only numerical ones, and you have to be aware of the stability and convergence limitations of numerical solutions.
