# FILE dlambda1dmuX2mpl2.txt
phi2 := z-> arctan(1/sqrt(z))/sqrt(z);
plot([phi2(z), 1/(z+1)], z = .125 .. 8, color = [red, green])
#
# Next bit for N=2 Isoperimetric Theorem
factor(diff(phi2(z), z)+phi2(z)/(2*z));
dmuYdmuX := simplify(solve(diff(phi2(muX)*phi2(muY(muX)), muX) = 0, diff(muY(muX), muX)));
dlambda1dmuX:= simplify(solve(diff(phi2(muX)*phi2(lambda1(muX)-muX), muX) = 0,
diff(lambda1(muX), muX)));
with(plots, implicitplot, display, odeplot);
ans := dsolve([diff(lambda1(muX), muX) = dlambda1dmuX, lambda1(1) = 2],
lambda1(muX), range = 1 .. 10, type = numeric);
odeplot(ans);