How the following system of ODEs can be integrated or solved asymptotically for $u\rightarrow \infty$?
$$2 a'(u)=u x'(u),$$ $$4 a u x'(u)-4 y'(u)=-2 x(u) \big[u a'(u)+a(u)\big],$$ $$4 a u y'(u)-4 x'(u)=\big[u\lambda'(a)a'(u)+\lambda(a)\big]-2y(u)\big[u a'(u)+a(u)\big].$$ with initial conditions $$x(0)=y(0)=0, a(0)=-1/2,$$ and $\lambda(a)=a^3+\frac14 a$.
It looks unsolvable, however, recently I asked about the solution of similar equations and was very impressed that they can be solved analytically. This gives me some hope, in fact, I could integrate one equation. But I could not make further progress.