Searching solutions for differential equations

We focus on the following problem, posed by L. Fuchs: For which linear differential equations L(y) = y⁽ⁿ⁾ + a_n-1y^(n-1)+ ... + a₁y⁽¹⁾ + a₀y = 0 can one express the solutions in terms of solutions of linear differential equations of degree ≤ n? Gino Fano published in 1900 a remarkable paper on this theme. It seems to have been forgotten until M. F. Singer took up this theme around 1985 . He proved and disproved certain statements and conjectures of Fano. We will try to present a systematic treatment of Fano's paper, due to Nguyen Khuong Ann and myself.