Assume that the system of differential equations y′=−z3, z′=y3 with the initial conditions y(0)=1, z(0)=0 has a unique solution y=f(x), z=g(x) defined for real x. Prove that there exists a positive constant L such that for all real x,
f(x+L)=f(x),g(x+L)=g(x). functiondedifferential equationsystem of differential equatio