Geodesic
The analytical solution to linear nonautonomous systems of ordinary differential equations
Matematičeskoe modelirovanie, Tome 9 (1997) no. 8, pp. 105-109 
D. M. Babanakov; I. R. Suslov. The analytical solution to linear nonautonomous systems of ordinary differential equations. Matematičeskoe modelirovanie, Tome 9 (1997) no. 8, pp. 105-109. http://geodesic.mathdoc.fr/item/MM_1997_9_8_a9/
@article{MM_1997_9_8_a9,
     author = {D. M. Babanakov and I. R. Suslov},
     title = {The analytical solution to linear nonautonomous systems of ordinary differential equations},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {105--109},
     year = {1997},
     volume = {9},
     number = {8},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_1997_9_8_a9/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.