In general, no. No tools in the symbolic toolbox that I know of are currently set up to employ multiple cores. I might have missed something, but I've been a moderately heavy syms user over the years.
That may change with time of course, in fact I could argue there are a couple of problems which could easily benefit from multiple cores. The examples I would see most prominently are the factoring of large integers (which might employ perhaps a quadratic sieve or elliptic curve methods), or testing large integers for primality (which might employ the MIller-Rabin algorithm.) All of those algorithms would seem to have good potential as multi-threaded code.
As far as the solution of a first order linear ODE system with 50 variables, DON'T DO IT SYMBOLICALLY. Even if you had multiple cores, this is the kind of problem where you will not see sufficient benefit, even if you had hundreds of cores, AND the code really was multithreaded. That is the sort of problem you will need to solve numerically. Sorry. And that means of course, that ALL constants need to be provided in advance as numbers. Sorry again. Odds are, even with a thousand cores available, your computer will turn to dust before it finishes that computation in symbolic form.
