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Question: How to find invariants like this?

Question:How to find invariants like this?

Ex 95 Maple
invariant
June 30 2012
0



Question 1. After googled, x*diff(F,t)+t*diff(F,x) for two variables, how about three variables or general ?

Question 2.

if deal with on variables case using the example in

http://demonstrations.wolfram.com/AFunctionInvariantUnderAGroupOfTransformations/


F := (x^2-x+1)^3/((x^2)*(x-1)^2)-y;
G:=y*diff(F,x)=0;
sol:=solve(G,y);

F(H)-F = 0
sol:=solve(F,x);
H := simplify(subs(y=F, sol[1]));

all above code can not get the results as in the web site, how it do?

 

Question 3. Which group of transformation, what is its matrix?
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