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I am reading "Ten lessons I wish I had learned before I started teaching differential equations" by Gian-Carlo Rota. On item 4, he says:

Should we, then, let the students remain blissfully unaware of the existence of linear differential equations with non-constant coefficients? If not, is there anything we can say about such differential equations at the elementary level? From time to time I succumb to one of the untapped temptations of the theory of differential equations: differential algebra. No elementary presentation of this beautiful subject has ever been attempted, to the best of my knowledge; Cohen’s book of the twenties is the closest, and it is still eagerly (and secretly) read today. Let me stick my neck out and propose that two results of differential algebra might be appreciated even by students in an elementary course. I will state one by way of end of this already long lesson, and reserve the second one for the next lesson. I have always felt excited when telling the students that even though there is no formula for the general solution of a second order linear differential equation, there is nevertheless an explicit formula for the Wronskian of two solutions. The Wronskian allows one to find a second solution if one solution is known (by the way, this is a point on which you will find several beautiful examples in Boole’s text). But there is a more fundamental fact, which I will state in a mathematical form that needs to be bowdlerized if we ever decide to try it out on an elementary class. It states that every differential polynomial in the two solutions of a second order linear differential equation which is independent of the choice of a basis of solutions equals a polynomial in the Wronskian and in the coefficients of the differential equation (this is the differential equations analogue of the fundamental theorem on symmetric functions, but keep it quiet).

What is this Cohen's book he is mentioning? I tried to Google "Cohen Differential Algebra" and found this which is something that seems to be very old like he is describing but doesn't seems to be exactly about differential algebra. I also tried to search for the same tags on libgen with no success.

Red Banana
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    My best speculation would instead be Cohen's "An introduction to the Lie theory of one-parameter groups; with applications to the solution of differential equations". But that was published in 1911. (Possibly it refers to another edition but I've seen no confirmation of such.) – Semiclassical Aug 29 '21 at 01:11
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    Found this link which allows you to manually review the material online, to determine if Semiclassical's citation is accurate. – user2661923 Aug 29 '21 at 01:14
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    https://archive.org/details/anelementarytre02cohegoog – Will Jagy Aug 29 '21 at 01:15
  • @user2661923 Corrected. – Red Banana Aug 29 '21 at 02:16
  • @WillJagy Is it really that one? What's about "differential algebra" in it? – Red Banana Aug 29 '21 at 02:19
  • I don't see it; the Cohen in differential algebra (or, well, algebra) was https://en.wikipedia.org/wiki/Irvin_Cohen who certainly wrote no book in the 1920's. Also, the speech you are reading was transcribed by someone, so that the name Cohen might mean Cohn or similar. You might turn it around, look up differential algebra, see what Cohen's or similar might appear. – Will Jagy Aug 29 '21 at 02:27

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