Mathematica has a function called NDsolve which attempts to reduce/simplify/solve fully symbolically and then falls back on numeric methods. Never actually used it for anything real, but could have potentially avoided this situation.
Grad student here. I recently did the obvious NDSolve thing but Mathematica kept beachballing, and after heating up my computer tremendously returned an empty set. Turns out, my problem was really simple and I could solve it by hand.
These are SDEs. Mathematica doesn’t solve them. In the end I needed a way for a computer to solve them faster, as an analytical solution wasn’t really possible. Mathematica wi never provide such insights. Maybe one day it will?