to be clear: this isn't actually a differential equation problem, and i'm sorry if i was confusing. it just seems like one because i'm starting with initial conditions and assuming a solution of a form.

so, i'm sorry if i ended up disappointing you with that. ultimately, it's just linear algebra to find a very crude polynomial approximation (it's linear!), and it would be more complicated if i had more data. alas... 

at least it's simple enough to pass the dipshitz condition though, right? or maybe it's so simple it failed it...

(don't box my dipshitz condition in, man. you need to compensate for the intersectionality..)