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Question: Is all axioms in these forms are for differential equations

Question:Is all axioms in these forms are for differential equations

ComputerUser 535 Maple
group-theory
December 13 2013
0

f(f(z,a),b) = f(z, a + b) 

i googled this axiom is diff(x(t),t) = xi(f);

then i think 

diff(x(t),t$2) = xi(f);

is it f(f(f(z,a),b),c) = f(z, a + b+c) ?

then think again

whether  f(f(f(z,a),b),c) + f(f(z,a),b) = f(z, a + b+c)  is diff(x(t),t$2)+diff(x(t),t)= xi(f);

however do not know how to construct right hand side  f(z, a + b+c), this is my guess

any books teaching this?

 

i think that if any matrix group be created from  f(f(f(z,a),b),c) + f(f(z,a),b)

that can help to convert to differential equations

 

hope that there is a solvable group which can represent solvable differential equation or differential system

 

if xi is Infinitesimal in maple,

how to find Infinitesimal from f(f(z,a),b) = f(z, a + b) ?
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