Examples of Euler's ordinary differential equation in science

Question

This equation $x^{2}y''+Axy'+By =0$ is the Euler second order ordinary differential equation.

I am not interested in pure math but I like applied math and I am studying for a test and I find it very boring if it just is a differential equation of a special form which is solvable so does it have any application in sciences?If yes where?

I found several applications in less than a minute by googling (regular and google-books). Maybe the history of this differential equation will be even more of interest to you, given what you said, so you might want to ask about its history in the history of math and science stack exchange. But do some basic investigation first, to make sure looking at Wikipedia or web pages easily found by google searches doesn't give what you want. — Dave L. Renfro, Sep 12 '22 at 20:33
The wikipedia article doesnt provide application of the equation in sciences:https://en.wikipedia.org/wiki/Cauchy%E2%80%93Euler_equation — Miss Mulan, Sep 12 '22 at 20:36
And all the other websites explain how to solve the equation not where it is found in sciences. — Miss Mulan, Sep 12 '22 at 20:36
A possibly useful secondary reading text is Differential Equations with Applications and Historical Notes by Simmons (3rd edition, 2017). The Euler equation is discussed on p. 126, where the term "equidimensional" is used. Googling Euler + "equidimensional" + "differential equation" + "application" led me to (9th or 10th highest hit) (continued) — Dave L. Renfro, Sep 12 '22 at 21:28
What′s in a name: why Cauchy and Euler share the Cauchy–Euler equation by Parker (2016) (see also here), which might be worth looking over (especially the references). And maybe some of the other hits from the google search I gave will be of use. — Dave L. Renfro, Sep 12 '22 at 21:29
Regarding Simmons' ODE book that I mentioned above, a few minutes ago I happened to come across (by accident) this answer by MJD that highly recommends the book by Simmons. — Dave L. Renfro, Sep 18 '22 at 10:22

Examples of Euler's ordinary differential equation in science

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