When finding solutions of differential equations it is necessary to take into account the theorems on innovation and unity of solutions of equations. In case of non-fulfillment of the conditions of these theorems, the methods of finding solutions of the studied equations used in computational mathematics may give erroneous results. It should also be borne in mind that the Cauchy problem for differential equations may have no solutions or have an infinite number of solutions.
The author presents two statements obtained by the author about the denseness of sets of the Cauchy problem without solutions (in the case of infinite-dimensional Banach space) and with many solutions (in the case of an arbitrary Banach space) in the set of all Cauchy problems.
Using two examples of the Cauchy problem for differential equations, the imperfection of some methods of computational mathematics for finding solutions of the studied equations is shown.

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