The analytical solution to linear nonautonomous systems of ordinary differential equations

A method is presented for calculating the analytical solution to linear systems of ordinary differential equations with time-dependent coefficients on the basis of diagonalization of the system matrix. The diagonalization problem is a generalization of the eigenvalue problem considered in case of the autonomous ODE system, thus the analytical solution is obtained as a sum of linearly independent particular solutions forming the fundamental system of solutions. A system of the point reactor kinetics equations with the reactivity being a linear function of time is considered.