You're missing a multiplication symbol "*" after the last a.  However, even after correcting that, solve finds no solution for B,g,a.  The fact is that equations such as these with variables appearing both in exponents and outside them are very unlikely to have closed-form solutions. Given numerical values of the parameters b,k,t,w, you might get numerical solutions using fsolve.  For example:

> eqs:= {B*(B-1)*t^B+3*a*B*t^B-6*a+12*a^2 = 0,
    g*(g-1)*t^g+3*a*g*t^g+(6*a-12*a^2)*b*t^(B*(b-1)) = 0,
    -3*a^2/t^2-3*a*t^(B*b-2)*(a+B*b)+3*a*t^(g-2)*(a+g)+1/2*g*B*t^(g+B-2)+k^2*t^(-3*a*(1+w)) = 0};
> fsolve(eval(eqs, {b=1,t=2,k=3,w=4}));

{B = -11.70443667, a = .4933504884, g = -.1179980646}

OK: next, what's the volume of the hemisphere?

The metal is used to make the surface of the tank.  Assuming the thickness is the same everywhere, the amount of metal used is proportional to the surface area.  What is that?  Don't forget to include the bottom as well as the side and the hemispherical top.

OK: next, what's the volume of the hemisphere?

The metal is used to make the surface of the tank.  Assuming the thickness is the same everywhere, the amount of metal used is proportional to the surface area.  What is that?  Don't forget to include the bottom as well as the side and the hemispherical top.

By including the "extended" terms, what you're doing is introducing homogeneous coordinates. 
Suppose your original equation is

> eq1:= add(add(a[i,j]*x^i*y^j,i=0..2-j),j=0..2) = 0;

then you use the change of variables x = X/Z, y = Y/Z, and multiply by Z^2:

> eq2:= expand(Z^2 * subs(x=X/Z, y=Y/Z, eq1));

You can extract the 3 x 3 matrix using the Hessian of this with respect to X,Y,Z.

> M := 1/2* VectorCalculus[Hessian](lhs(eq2), [X,Y,Z]);

By including the "extended" terms, what you're doing is introducing homogeneous coordinates. 
Suppose your original equation is

> eq1:= add(add(a[i,j]*x^i*y^j,i=0..2-j),j=0..2) = 0;

then you use the change of variables x = X/Z, y = Y/Z, and multiply by Z^2:

> eq2:= expand(Z^2 * subs(x=X/Z, y=Y/Z, eq1));

You can extract the 3 x 3 matrix using the Hessian of this with respect to X,Y,Z.

> M := 1/2* VectorCalculus[Hessian](lhs(eq2), [X,Y,Z]);

Note that this help page (and the one in Standard GUI, but not Classic) writes the equation wrong:

Z(t).A(t).Z(t) has become Z(t)^2 A(t), because someone used commutative multiplication instead of the noncommutative "." and automatic simplification took over.

I've submitted an SCR.

Note that this help page (and the one in Standard GUI, but not Classic) writes the equation wrong:

Z(t).A(t).Z(t) has become Z(t)^2 A(t), because someone used commutative multiplication instead of the noncommutative "." and automatic simplification took over.

I've submitted an SCR.

You want RootOf, not Rootof.  Also, you need to tell it the variable, z.

You want RootOf, not Rootof.  Also, you need to tell it the variable, z.

The solution does not go to 0 at infinity.  This is a fact, which I told you already.  No rewriting will change it.  I don't know what you're hoping to accomplish by writing ln(r/r[max]) instead of ln(r): this subtracts a constant, but you won't have a solution of the differential equation any more.

The solution does not go to 0 at infinity.  This is a fact, which I told you already.  No rewriting will change it.  I don't know what you're hoping to accomplish by writing ln(r/r[max]) instead of ln(r): this subtracts a constant, but you won't have a solution of the differential equation any more.

Yes, it works under Vista too.  Absolutely no problem.

Hmm... Well, I _thought_ this was the situation, but it seems that it's more complicated.  It is still true that PostScript is a 2d format, and that the PostScript file contains no information about the third dimension.  But it's not simply a matter of drawing the image back-to-front.

In Maple 13 Standard, it looks like for 3d plots the Standard worksheet renderer is actually used to produce a bitmap image which is saved to the PostScript file.

No, PostScript is inherently 2-dimensional.  The "back-to-front" effect is simply the result of the order in which the elements are rendered, with the later ones overwriting the earlier ones.

Make sure you spelled it right.  Maple is case-sensitive.