How does one obtain all solutions from dsolve? I see an option called Allsolutions, but this seems to only apply to solve and other functions. It does not work with dsolve.

For example, maple gives one solution for the following first order non-linear ODE. But the ODE has another solution y(x)=0 as well. How does one tell Maple to return all solutions? I am interested in this when using the 'implicit' option mainly. Here is an example

restart;
num:=-(exp(x)*sin(y(x))-2*y(x)*sin(x)):
den:=(exp(x)*cos(y(x))+2*cos(x)):
eq:=diff(y(x),x)=num/den;

r0:=dsolve(eq,y(x));

But when I tried y(x)=0, it turned out to also be a solution

odetest(y(x)=0,eq);
                          0

But dsolve did not return this solution on its own along with the first one.  But on another example, Maple did well, and returned all solutions. Here is the other example

eq:=(2*x*y(x)^2+2*y(x))+(2*x^2*y(x)+2*x)*diff(y(x),x);
dsolve(eq=0,y(x),'implicit');

In the above, Maple returned the two solutions. 

Is there a correct way to tell Maple dsolve to return all solutions all the time? Why did it return both solution in the above example, but not in the first example?

I am maple newbie. Thank you.

in Mathematica, there is the option called BoxRatios

"is an option for Graphics3D that gives the ratios of side lengths for the bounding box of the three‐dimensional picture."

It is sort-of like aspect ratio, but for 3D. It is set by default so make 3D plot looks "nice". I can't seem to find equivalent Maple option. The closest is the option "s=" for plot3d, but this just turns of/on "constrained scaling" and does not allow one to modify the "BoxRatios"

Let me give an example. Here is 3D plot in Mathematica and the same in Maple. I'd like to get the Maple 3D to look similar to Mathematica 3D in terms of the "aspect ratio". Maple on the z-axis is using the same size as in the x and y axis, and even though this is realistic, it does not make the plot as nice. I want to change this ratio.

T0[x_, y_, m_] :=20/Pi Sum[ (-1)^(n + 1)/n Exp[- (n Pi/10) y] Sin[ (n Pi/10) x], {n,1, m}]
Plot3D[T0[x, y, 70], {x, 0, 10}, {y, 0, 10}, PlotRange -> All,  AxesLabel -> {x, y, z}]

In Maple:

T0:= (x,y,m)-> 20/Pi*sum( (-1)^(n+1)/n*exp(- n*Pi/10*y)*sin(n*Pi/10*x),n=1..m);
plot3d(T0(x,y,50),x=0..10,y=0..10,scaling=unconstrained);

So Maple is using 1:1:1 box ratio. Mathematica default is 1:1:0.4, and I wanted to see if I can change Maple to be the same.

I get same plot in Maple using scaling=unconstrained or scaling=constrained. So this option is not very useful for what I want.

Is there a way to change the "BoxRatios" as defined above in Maple? There must be, right? Do I need to use different package?

How can one find out when a Maple command or package became part of Maple? i.e. which Maple version first had this command or package?

For example, I'd like to know when applyrule https://www.maplesoft.com/support/help/Maple/view.aspx?path=applyrule was introduced. But this applies really to any command I see.

In Mathematica, this is easy to find out, since it is documented in the help page for the command, at the botton of each page when the command was added. Is there a command or a web page that shows this type of information about Maple commands and packages?

This came up in another language. I tried to solve it in Maple, but I am newbie so did not know how to.

The problem is to remove all products of  "a^n*b^m" that shows up in an expression, including any powers of "n,m". For example, given these three expressions

f0 := a^4+4*a^3*b +6*a^2*b^2+4*a*b^3+ b^4;
f1 := 3*(a*b -2*c);
f2 := (a*b -2*c)/(c - a*b);

Then applying the transformation needed, will result in

f0:= a^4+b^4;
f1:=-6*c;
f2:=-2;

Becuase the transformation will detect any a^n*b^m and simply replace this product by zero 
from the resulting expression. So "a*b^2 + 2" will become "2", and so on.

I assume a function such as "patmatch"  or "match" is needed. I tried, but could not figure how. 
I also tried algsubs. How would this be coded in Maple?

I did not understand fully some of the notation used in 2D when I had the tools->options->Display->Output display->2D. So I thought if I change it to Maple notation. I might see what the symbol actually mean.  But when I did so, the result was even more confusing. Full of typesetting:-mrow commands and hard to read.

Here is the output in 2D

restart;
int(1/( (x-a)*(x-b)),x=-infinity..infinity  );

And here is the output when I switched to Maple output:

I was expecting to see "normal" looking Maple commands, which I can understand. Even the Latex is easier to read than the above mumple jumple code:

Does this mean one should forget about using Maple notation for output from now on? Why is it the output so complicated?