Abstract:
The equation $Ay^{\prime}+By=f(t)$, where $A$ and $B$ are square matrices has been considered. The solution has been sought in such a class of vector functions, the components of which with their derivatives increase in infinition not faster than any degree of $t$. The case $\det A=0$ has been considered. The sufficient and necessary conditions of the solution-existence for initial and general initial problems have been obtained.
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