Abstract
All the subalgebras of first-order symmetry operators for the d'Alembert equation, generating the bases of solutions in the method of noncommutative integration of linear differential equations, which cannot be constructed in the method of separation of variables, are found. These bases themselves are then given in explicit form. The complete systems of solutions of the d'Alembert equation, determined by noncommutative sets of first-order symmetry operators, are thereby classified.
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