On the solution of a problem of transport theory (Q1309084)

The matrix system (1) \({dx \over d \tau}=-AX (\tau)+L^ +X(\tau)+L^ - Y(\tau)\), \(-{dY \over d \tau}=-AY (\tau)+L^ -X(\tau)+L^ +Y (\tau)\), \(\tau \geq 0\), is investigated. It is supposed that the matrices \(A\), \(L^ \pm\) are such that \(Y(\tau)=\rho X (\tau)\), where \(X(0)=E\), \(Y(0)=\rho\). The system (1) is generated by a discrete model of stationary scattering in a homogeneous slab.