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 Solvability of ODEs describing curves on $\mathbb{S}^2$ or $\mathbb{H}^2$ Commun. Korean Math. Soc.Published online May 12, 2021 Hyungjin Huh Chung-Ang University Abstract : We show the solvability of the ordinary differential equations describing curves on sphere or hyperbolic space. Making use of the geometric properties of the equations, we derive explicit solution formulae. Keywords : curves on sphere, curve on hyperbolic space, explicit solution formula MSC numbers : 35B40, 35C05, 35Q41 Full-Text :