A formulation of the time dependent molar balance equations, one of which is a nonlinear Bernoulli differential equation, is a preliminary step to modeling an isothermal semi-batch reactor with irreversible second-order reactions. The molar balance equations obtained in this fashion are classified as first order nonlinear ODEs. This paper presents a methodology to replace the nonlinear ODE that characterizes the molar composition of the reactants with an equivalent, linear ODE derived from a Bernoulli ODE to obtain an analytical solution. This approach leads to a general solution. The analytical results using this methodology are subsequently compared to numerical solutions to verify the accuracy of the model. (C) 2015 Elsevier Ltd. All rights reserved.