Solvability of equations by quadratures and Newton's theorem
Let \(F\) be an ordinary differential field and let \(L(y)=0\) be a linear homogeneous differential equation over \(F\). There is an effective dating back to Liouville criterion of solvability in quadratures of the equation. Namely the equation should have a non-trivial solution \(u\) such that \({u}'=au\), where \(a\) is algebraic over \(F\). The author considers that the proof of this fact in the framework of differential algebra is rather involved and offers a simpler proof in the case when \(F\) is a functional differential field.
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