2019-02-182019-02-182018-06-28PORTUGAL, Izaque Pantoja. Solvabilidade de soluções via Nagumo e Osgood para o problema x0 = f(t; x). 2018. 66 f. Trabalho de Curso (Licenciatura em Matemática) – Faculdade de Ciências Exatas e Tecnologia, Universidade Federal do Pará, Abaetetuba, 2018. Disponível em: http://bdm.ufpa.br/jspui/handle/prefix/1038. Acesso em:.http://bdm.ufpa.br/jspui/handle/prefix/1038This work appeared of the result of the scientific initiation research of the book of renowned Dro Luiz Adauto da Justa Medeiros about Ordinary Differential Equations, because in his book he makes a qualitative study of the differential equation to climb x0 = f(t; x), specifically will approach the study of uniqueness of solutions of a differential equation of first order of a qualitative point of view. For such we will exhibit the solution definitions, and we will make a basic study of metric spaces, with focus in complete metric spaces and the sequences of Cauchy. We showed a little of the history of Mathematicians Willian Foog Osgood and Mitio Nagumo and we exhibited their conditions of uniqueness for the solution of the problem x0 = f(t; x)Acesso AbertoUnicidade de soluçãoProblema de CauchyTeorema de NagumoTeorema de OsgoodUniqueness of solutionsProblem of CauchyTheorem of NagumoTheorem of Osgood.CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICATrabalho de Curso - Graduação - Monografia