[gus_massa]

Luckily there are many interesting examples that can be solved. In particular the linear differential equations. Many equations can be approximated by a linear version of it.

Also, in Physics, a lot of ODE are mysteriously integrable if the variable is x instead of t. (One reason is that it's easy to measure the force/fields, but the "real" thing are the potential, so you are measuring the derivative of a hopefully nice object.)

Also a lot of the theoretical advanced stuff to prove analytical solutions and to estimate the error in the numerical integrations use the kind of stuff you learn solving the easy examples analytically.

And also historical reasons. We have less than 100 years of easy numerical integrations, and the math curriculum advance slowly. Anyway, I've seen a reduction in the coverage of the most weird stuff like the substitution θ=atan(x/2) (or something like that, I always forget the details). It's very useful for some integrals with too many sin and cos, but it's not very insightful, so it's good to offload it to Wolfram Alpha.