something like this?:

d:= x^2*(diff(y(x), x, x))+x*(diff(y(x), x))+(x^2-1/4)*y(x);
map((u->collect(u,y),expand)@(u->u/x^2),d);
                             d
                / 2      \   -- y(x)
                |d       |   dx        /     1  \
                |--- y(x)| + ------- + |1 - ----| y(x)
                |  2     |      x      |       2|
                \dx      /             \    4 x /

you can generate the determining system like:

with(PDEtools):
d1:=diff(x(t),t)=2*x(t)*y(t)^2:
d2:=diff(y(t),t)=-y(t)-x(t)^3:
DeterminingPDE({d1,d2});
   d                        /       3  /d                  \
  {-- _xi[1](t, x, y) = 1/2 |(-y - x ) |-- _eta[1](t, x, y)|
   dt                       \          \dy                 /

                 3      4  2  /d                 \
         + (2 x y  + 2 x  y ) |-- _xi[1](t, x, y)|
                              \dy                /

           /d                  \        2 /d                  \
         + |-- _eta[1](t, x, y)| + 2 x y  |-- _eta[1](t, x, y)|
           \dt                 /          \dx                 /

                                                        2
         - 4 _eta[2](t, x, y) x y - 2 _eta[1](t, x, y) y

              2  4 /d                 \\   /     2
         - 4 x  y  |-- _xi[1](t, x, y)||  /  (x y ),
                   \dx                // /

        d                         /  3     2 /d                  \
        -- _eta[2](t, x, y) = 1/2 |(x  + y)  |-- _eta[1](t, x, y)|
        dt                        \          \dy                 /

                  3  /d                  \       /
         + (-y - x ) |-- _eta[1](t, x, y)| - 2 y |
                     \dt                 /       \

              3      /d                  \
        y x (x  + y) |-- _eta[1](t, x, y)|
                     \dx                 /

              4        2  /d                  \
         + (-x  y - x y ) |-- _eta[2](t, x, y)|
                          \dy                 /

              3  2 /d                  \
         + 2 y  x  |-- _eta[2](t, x, y)|
                   \dx                 /

              2        3
         + (-y  + 2 y x ) _eta[1](t, x, y)

                     3                    \\   /     2
         - 2 (y/2 + x ) x _eta[2](t, x, y)||  /  (x y )}
                                          // /

You may try something like:

plots:-logplot(exp(2*x), x=-10..0);

See ?worksheet,documenting,2DMathDetails

was already posed by Joe Riel here, a year and a half ago. I wonder whether he has found the solution.

Sometimes I use a script with the line:

maple-path/maple -x  $1

and open the worksheet like on the command line as:

script-name file.mw

but most practical for me is a button in Krusader, my preferred file manager: select the worksheet, click the button, and Maple opens with this worksheet.

Not yet another worksheet in another tab...

Executing these lines I get a lot of error boxes with messages like:

Attempted to set property of unknown component 'TextArea0'

or with retrieve instead of set. This is Maple 12 on Win XP

I do not know if "decent", but one way to do it is:

b:=<2/8,1/9>:
R:=<<-2,-1>|<-3,-6>>;
with(LinearAlgebra):
solution1:=simplify(LinearSolve(R,-b));
seq(assign(X||i,solution1[i]),i=1..op(1,solution1));
X1;X2;
                                 7/54


                                 -1
                                 ---
                                 324

You can do this:

qs := c1*(1/(H-B)^(7/3)*abs(q)^2/ks^2/Delta/Ds)^(3/2)*
(1/(H-B)^(7/3)*abs(q)^2/ks^2/Delta/Ds/tr)^(71/5)*
signum(q)*(Delta*GRAVIT*Ds^3)^(1/2);

algsubs(op([1,1],indets(qs,`^`(anything,3/2)))=u,qs):
simplify(%) assuming u>0,tr>0;
subs(u=op([1,1],indets(qs,`^`(anything,3/2))),%);

c1*(1/(H-B)^(7/3)*abs(q)^2/ks^2/Delta/Ds)^(157/10)/tr^(71/5)*signum(q)*(Delta*GRAVIT*Ds^3)^(1/2);

q, ks, lf? The roots are a function of them. Without additional information on these parameters it is impossible to decide if a solution is real.

is nicer:

with(PDEtools,dchange):
de3 := 20*a^2*diff(w(a),a)^2-8*a^2*diff(diff(w(a),a),a)*w(a)+w(a)^6*(a-1)*(a+1);
d4:=dchange({a=x,w(a) = W(x)/(1-ln(x))},de3);
s4i:=dsolve(d4,implicit);
subs(1/(-1+ln(x))^4=v,s4i):
collect(%,[_C1,_C2],distributed,c->collect(c,[v,W,x],factor));
s4i2:=subs(v=1/(-1+ln(x))^4,%);

s4i2 := ((-1/(336*x^2)+1/336)*W(x)^7-1/12*(2*ln(x)-3)*(-1+ln(x))^2/x^2*W(x)^3+3/2*(-1+ln(x))^3/x*W(x)^2+5/2*(-1+ln(x))^4*(-1+ln(W(x)))*W(x))/(-1+ln(x))^4-x-W(x)*_C1-_C2 = 0;

But if this is the solution, 'odetest' does not seem able to verify it without additional help.

You solve for f(x)=g(x), like

solve(x=2*x^3,x);
                               1/2     1/2
                              2       2
                           0, ----, - ----
                               2       2

but I read that this wicd has to do with WEP, and quite frequently Maple 12 Classic crashes under WinXP in my home machine producing simultaneously a WEP "application error".

at least a power solution can be obtained:

with(PDEtools,dchange):
d1:=(a^2-1)*diff(y(a),a)^6-8*a^2*diff(y(a),a,a,a)*diff(y(a),a)+20*a^2*diff(y(a),a,a)^2;
dchange({a=sqrt(1-u),y(a)=Y(u)},d1):
expand(%):
d2:=collect(%,diff,factor@(v->v/16));

d2 := 4*u*(-1+u)^3*diff(Y(u),u)^6+(5-5*u)*diff(Y(u),u)^2+(-8*(-1+u)^2*diff(Y(u),`$`(u,2))+8*(-1+u)^3*diff(Y(u),`$`(u,3)))*diff(Y(u),u)-20*(-1+u)^3*diff(Y(u),`$`(u,2))^2;

Order:=4:
dsolve(d2,Y(u),series);
                                  (2)         2
  Y(u) = Y(0) + D(Y)(0) u + 1/2 (D   )(Y)(0) u  +

                  (2)                           2        (2)       2
             -8 (D   )(Y)(0) D(Y)(0) + 5 D(Y)(0)  + 20 (D   )(Y)(0)
        1/48 -------------------------------------------------------
                                     D(Y)(0)

         3      4
        u  + O(u )