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][1] 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


  [1]: http://dlmf.nist.gov/31