Not sure how much you’d care, but I came back to this and found (by hand) a function which closely approximates the solution - it’s not exact but it’s also not super far. Graph.

I think I could also solve the differential equation by hand at this point (getting the same solution as before) - I haven’t, but I’m pretty sure I could if I wanted to for whatever reason. I’m doubtful it’s possible to get an exact solution in terms of just x but if you ever manage I’d love to see how.