[Integration of the Ludwig v. Bertalanffy's growth differential equation. I]

The growth differential equation of v. BERTALANFFY, (formula; see text) has no closed (analytic) general solution for any given values of m and n. Only for n = 1 and any m, the v. BERTALANFFY's equation is a BERNOULLI's one which is soluble without difficulties. If m and n both are rational numbers, the equation is soluble in all cases but the integrals are members of very different classes. In this paper, some methods are demonstrated to integrate the equation for rational m and n if delta = m - n = 1 up to the exponents' denominator four. For any numerically given real m, n, the transformation of CONTE may render possible to find a reduced form of the primarily given equation which can be solved by a range of analytical terms.