Can Cayley table be converted to function ?

What can Cayley table use in Maple?

after composite

test5 := subs(y=-q/p, subs(x=-q/p, x+y));
test6 := subs(p=x,subs(q=y,test5));

how to recover test6 := -2*y/x back to x+y with y/x or x/y;

any general method to eliminate the derivative of lambda1,lambda2,lambda3

a:= -(diff(lambda1(t), t))+lambda3(t);
b:= -lambda1(t)-(diff(lambda2(t), t))+4*lambda3(t);
c:= -lambda2(t)+3*lambda3(t)-(diff(lambda3(t), t));

result in 2*lambda1(t) - lambda2(t) + 2*lambda3(t) = 0;

f := Diff(u(t),t$2)+Diff(u(t),t)+u(t)+x(t);

after indicate to extract u(t), should output Diff(u(t),t$2)+Diff(u(t),t)+u(t)

after indicate to extract x(t), should output x(t)

eqt := y^5+y^4 + -0.5109*y^3 + -0.0595*y^2 + 0.0000-(-3.1086e-015*u^4 + u^3 + -0.5109*u^2 + -0.0595*u) = 0;

solve({eqt, y=m*t+c, u=n*t+d}, {y, u}, 'parametric');

solve({y^5+y^4 + -0.5109*y^3 + -0.0595*y^2 + 0.0000-(-3.1086e-015*u^4 + u^3 + -0.5109*u^2 + -0.0595*u) = 0, u=t}, [x,y]);

solve(eqt, [y(t), u(t)])

algcurves[parametrization](eqt, y, u, t);

all trials i failed