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I am currently on the lookout for good motivational examples for differential Galois theory, and I was wondering the following:

Is there a book or article devoted (either partially or completely) to the computation of differential Galois groups of various "classical" differential equations, or families of differential equations?

For example, one could think of Euler's differential equation, the Legendre differential equations, Bessel's differential equation, etc. (Of course, just browsing through the literature on differential Galois theory one encounters a fair number of examples along the way, but it would be nice to have a single text with as many examples as possible.)

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    $\begingroup$ This doesn't seem to cover quite all you are looking for, but maybe it helps: arxiv.org/abs/0712.4124 $\endgroup$
    – Yaakov Baruch
    Commented Oct 26, 2016 at 20:32

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