In this paper, the differential calculus was usedudto obtain some classes of ordinary differential equations (ODE)udfor the probability density function, quantile function, survivaludfunction and hazard function of Cauchy, standard Cauchy andudlog-Cauchy distributions. The distributions are related byudlogarithmic transformation. The ODEs for the inverse survivaludfunction and reversed hazard functions of the distributionsudwere not considered because of their nature and complexity.udThe stated necessary conditions required for the existence ofudthe ODEs are consistent with the various parameters thatuddefined the distributions. Solutions of these ODEs by usingudnumerous available methods are a new ways of understandingudthe nature of the probability functions that characterize theuddistribution
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