Abstract:
In this paper, we find sufficient conditions for the solvability by quadratures of J. Bernoulli's equation defined over the set $M_2$ of square matrices of order 2. We consider the cases when such equations are stated in terms of bases of a two-dimensional abelian algebra and a three-dimensional solvable Lie algebra over $M_2$. We adduce an example of the third degree J. Bernoulli's equation over a commutative algebra.
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