In this paper, the differential calculus was used
to obtain some classes of ordinary differential equations (ODE)
for the probability density function, quantile function, survival
function, inverse survival function, hazard function and
reversed hazard function of the Frĕchet distribution. The
stated necessary conditions required for the existence of the
ODEs are consistent with the various parameters that defined
the distribution. Solutions of these ODEs by using numerous
available methods are a new ways of understanding the nature
of the probability functions that characterize the distribution.
The method can be extended to other probability distributions
and can serve an alternative to approximation
