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Some information on Pietro's ODE: $$ (4x^3-136x^2+4x)u''+(8x^2-204x+4)u'+(x-10)u=0 \tag{1}$$ I will use this notation: $$ c := (1+\sqrt{2}\;)^4 = 17+12\sqrt{2} \approx 33.97056 , \\ c_o := \frac{1}{c} = 34-c = 17-12\sqrt{2} \approx 0.02944 , \\ a := 1-c^2 = -576-408\sqrt{2} \approx -1159.9991 , \\ q := -\frac{11317}{4}-234\sqrt{2} \approx -660.176 , \\ \alpha := \frac{3}{2}, \beta := \frac{3}{2}, \gamma := \frac{3}{2}, \delta := 1, \epsilon := \frac{3}{2} . $$ Maple converts $(1)$ to a Heun differential equation, and evaluates it in terms of the Heun functions. See DLMF for information on that. I will follow their notation. In interval $(c_o,c)$, two linearly independent solutions of $(1)$ are $$ u_1(x) = $$ TO BE CONTINUED