This work is to solve an infinite 2-system model of first order ordinary differential equations. The system is in Hilbert space l2 with the coefficients are any positive real numbers. The system is rewritten as a system in the form of matrix equations and it is first studied in ℝ2 where its solution is obtained and a fundamental matrix is constructed. The results are carried out to solve the infinite 2-system in Hilbert space l2. The control functions satisfy integral constraint and are elements of the space of square integrable function in l2. The existence and uniqueness of the solution of the system in Hilbert space l2 on an interval time [0, T] for a sufficiently large T is then proven.
