Prove that the solution you found is unique provided u lies in the domain D

u (t) = u(t) u (t) u(t) (u1(t)2 + u3(t)2)3/2 uz(t) = us(t) u(t)= uz (t) (u1(t)2 + u3(t)2)3/2 with initial condition u(0) = [1,0,0, 1]T. Prove that the solution you found is unique provided u lies in the domain D = :{u: 1/4 < u + u}}. Hint: Bound the Frobenius norm of the Jacobian of f with respect to u, where the Frobenius norm ||A||F of a matrix A is given by the Euclidean (vector) norm of the vector consisting of all entries of A, i.e., || A|| F = Aij|.