What you say is important, but far from sufficient. Recipes which serves as exercises at one level serve as building blocks for the next level. I would argue th

What you say is important, but far from sufficient. Recipes which serves as exercises at one level serve as building blocks for the next level. I would argue that the reason it is important to understand the solutions of a few typical forms of differential equations is that they correspond to problems that show up in many different contexts. So not only can the solution methods be applied in all those contexts, but also the intuition for that class of problems/solutions ports over nicely, and allows you to use these as building blocks in bigger systems. > Because in this way you can obtain solution to any DE with any degree of precision (within reasonable assumptions about complexity of the problem). IMHO one of the key goals of education is exactly to understand why/when this is not the case, so you don't shoot yourself in the foot. Numerical methods will often generate junk results (too many examples to count, of people running useless simulations to problems whose solutions don't exist, or algorithms don't converge, so that the results of numerics are fundamentally misleading). Further, probably one of the most valuable topics is an understanding of linear differential equations (and linear shift-invariant systems more generally), including typical solutions and how they compose. A huge chunk of our science & engineering knowledge is built on this edifice. This is hardcore theoretical stuff (ideas & concepts), that can't be derived from being able to numerically solve differential equations. Further, a solid understanding of these concepts allows one to decompose a problems solutions into eigen-modes, and build much better solvers specialized to a situation.