For a singular Cauchy problem

where *N* ≥ 2 and *a*_{
ijk
} are constants, *a*_{00k} = 0, k ∈ {0, 1, . . .,*N*} , *a*_{100} ≠ 0, *a*_{010} ≠ 0, *a*_{
ijk
} = 0, 1 ≤ *i* + *j* < *m*, *k* ∈ {1, . . . ,*N*} , 2 ≤ *m* ≤ *N*, and *φ* is a function small in a certain sense, we find a nonempty set of continuously differentiable solutions *x*: (0, *ρ*] → ℝ, where *ρ* is sufficiently small, such that

where *c*_{1}, . . . , *c*_{
m
} are known constants.

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Translated from Neliniini Kolyvannya, Vol. 20, No. 2, pp. 166–183, April–June, 2017.

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Zernov, A.E., Kuzina, Y.V. Singular Cauchy Problem for an Ordinary Differential Equation Unsolved with Respect to the Derivative of the Unknown Function.
*J Math Sci* **231**, 712–729 (2018). https://doi.org/10.1007/s10958-018-3846-5

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DOI: https://doi.org/10.1007/s10958-018-3846-5