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Abstract  In this paper, we present a complete algorithm to decompose nonlinear differential polynomials in one variable and with coefficients in a computable differential field $${\mathcal K}$$ of characteristic zero. The algorithm provides an efficient reduction of the problem to the factorization of LODOs over the same coefficient field. Besides arithmetic operations, the algorithm needs decomposition of algebraic polynomials, factorization of multi-variable polynomials, and solution of algebraic linear equation systems. The algorithm is implemented in Maple for the constant field case. The program can be used to decompose differential polynomials with thousands of terms effectively. [ABSTRACT FROM AUTHOR]