O16-071
> restart;
> ed:=(x^2-x)*diff(y(x),x$2)-3*x*diff(y(x),x)+3*y(x);

                         / 2      \
                  2      |d       |       /d      \
          ed := (x  - x) |--- y(x)| - 3 x |-- y(x)| + 3 y(x)
                         |  2     |       \dx     /
                         \dx      /

> with(DEtools):  odeadvisor(ed);

               [[_2nd_order, _with_linear_symmetries]]

> sol:=dsolve(ed,y(x));

                                      3      2
      sol := y(x) = _C1 x + _C2 (1/2 x  - 3 x  + 1 + 3 ln(x) x)

> ed1:=simplify(subs(y(x)=x*v(x),ed));

  ed1 :=

                           / 2      \                      / 2      \
          2 /d      \    3 |d       |       /d      \    2 |d       |
        -x  |-- v(x)| + x  |--- v(x)| - 2 x |-- v(x)| - x  |--- v(x)|
            \dx     /      |  2     |       \dx     /      |  2     |
                           \dx      /                      \dx      /


> s:=subs(sol,y(x));z:=unapply(s,x);t:=D(z);

                                  3      2
           s := _C1 x + _C2 (1/2 x  - 3 x  + 1 + 3 ln(x) x)


                                    3      2
        z := x -> _C1 x + _C2 (1/2 x  - 3 x  + 1 + 3 ln(x) x)


                                     2
           t := x -> _C1 + _C2 (3/2 x  - 6 x + 3 + 3 ln(x))

> {z(1)-a,t(1)};# Sauf pour a=0, il n'y a pas de solution

                  {_C1 - 3/2 _C2, _C1 - 3/2 _C2 - a}

> dsolve( {ed, y(1)=a, D(y)(1)=1}, y(t));
> DEplot(ed,y(x),
> x=1.5..2.4,[[y(2)=-1,D(y)(2)=1]],y=-4..5,stepsize=.05);


>