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I think that the questionner could be addressed to the mathematical subject named Differential Galois Theory.

A first accessible reading could be J.F. Ritt "Integration in finite terms. Liouville's theory of elementary methods", Columbia University Press, 1948.

The corresponding google wikipedia page could be another starting point. http://en.wikipedia.org/wiki/Differential_Galois_theory

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I think that the questionner could be addressed to the mathematical subject named Differential Galois Theory.

A first accessible reading could be J.F. Ritt "Integration in finite terms. Liouville's theory of elementary methods", Columbia University Press, 1948.

The corresponding google page could be another starting point. http://en.wikipedia.org/wiki/Differential_Galois_theory

show/hide this revision's text 1

I think that the questionner could be addressed to the mathematical subject named Differential Galois Theory. A first accessible reading could be J.F. Ritt "Integration in finite terms. Liouville's theory of elementary methods", Columbia University Press, 1948.