[has2k1]

The article is not questioning the "theory", the identified problem is the teaching at undergraduate level. As it was/is commonly taught, it is neither pure nor applied. Rather it is categorisations and tricks, little of which has any practical value.

As a body of work Differential equations are so messy that theorists landed on so many disparate results. As such Differential equations courses are commonly taught as a "survey of the land" type of courses, so they tend to be incoherent. On the other hand if the teaching focused on practicality there is a lot of commonality among the practical cases.