Differential Invariants and First Integrals of the System of Two Linear Second-Order Ordinary Differential Equations

In a recent paper the basis of algebraic invariants of the system of two linear second-order ordinary di_erential equations has been found. Now we obtain the di_erential invariants for this family of equations, which depend on the _rst-order derivatives. It is shown that the _rst integrals of such systems can be sought as the functions of the algebraic and di_erential invariants of a given system. Di_erential invariants can be useful also in constructing the transformation connecting two equivalent systems when their algebraic invariants are constant.