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Using the compatibility condition for the Painlevé equations, several new fourth-order ordinary differential equations (ODEs) that are analogies of the Painlevé equations are found. The isomonodromic linear problems for these equations are given. Special solutions of the fourth-order ODEs found are discussed. The Painlevé test is applied to investigate several fourth-order ODEs.doi:10.1088/0305-4470/35/21/310 fatcat:h4dse5jo2vau7h7thr7s3vsmyu