The radial second-order differential equations of the theory of collisions between atomic systems plus the boundary conditions at infinity are transformed to an equivalent system of first-order differential equations by introducing for each channel the Wronskian of the wavefunction and the Jost solution of the uncoupled equation (incoming and outgoing Jost solutions for open and closed channels, respectively). In the asymptotic region the Wronskian gives directly the value of the corresponding S-matrix element. By using the first-order Magnus-Fer approximation an approximate analytical expression for the S-matrix elements of the multichannel problem is obtained; the formula is also particularised to the two-channel problem.