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