_Envdiffopdomain := [Dx,x]:  # Must tell the code what our variable name is
			     # and what the name for d/dx is.
with(DEtools):

L1 := Dx^3+1/6*(26*x-9)/x/(x-1)*Dx^2+1/27/x*(76*x-55)/(x-1)^2*Dx+28/729/x/(x-1)^2;

L2 :=
x^2*(27*x^8-5*x^5+54*x^4+15*x+27)*(27*x^8+4*x^5+54*x^4+27)*Dx^3-3*(-684*x^9-\
846*x^5+1944*x^12+162*x^13+729*x^16-10*x^10-243+1458*x^8-50*x^6)*x*Dx^2+(-1662
*x^9-60*x^6+2916*x^7-81-777*x^5+295*x^13-3726*x^4+729*x^3+1917*x^16-180*x+4374
*x^11+270*x^12-5292*x^8+729*x^19-20*x^10+2916*x^15)*Dx+(2535*x^6+4104*x^5+160*
x^7+3645*x^4+729+3645*x^16+2592*x^9-371*x^14+1759*x^10+7290*x^12-648*x^13+729*
x^20+7290*x^8+405*x^2+1620*x-756*x^17)*x;

L3 := x^3*(16*x^6+48*x^5+144*x^4+216*x^3+81*x^2+972*x+729)*(4*x^3+27)*Dx^3+6*(2*
x+3)*(24*x^8+52*x^7+234*x^6+189*x^5+54*x^4+3645*x^3-1458*x^2+2916*x+6561)*
x^2*Dx^2+(64*x^10+384*x^9+1584*x^8+4896*x^7+5940*x^6+9396*x^5+54189*x^4+
43011*x^3+37179*x^2+118098*x+137781)*x*Dx+128*x^10+640*x^9+2400*x^8+3600*x^7
+2376*x^6+28512*x^5+28674*x^4+12393*x^3+76545*x^2+78732*x+39366;

L4 := Dx^3+1/3*(13*x-7)/x/(x-1)*Dx^2+2/27/x*(38*x-35)/(x-1)^2*Dx+28/729/x/(x-1)^2;

L5 := Dx^3+1/3*(11*x-5)/x/(x-1)*Dx^2+2/27/x*(23*x-20)/(x-1)^2*Dx-10/729/x/(x-1)^2;

# At the moment, Maple does not solve these equations. For example:
eq1 := diffop2de(L1,y(x));
dsolve( eq1 );

read impr_order3:

# All of them are irreducible with imprimitive Galois group. Liouvillian solutions:
order3(L1);
order3(L2);
order3(L3);
order3(L4);
order3(L5);