ABSTRACT
This chapter presents methods to solve problems with one independent variable involving the first-order differential equation and the second-kind boundary condition. Mathematically, this class of cases can be summarized as second-kind boundary condition. The chapter examines the problem of heating of a sold and heat conduction through a spherical shell with constant heat flux at external surface and constant temperature at internal face. The solutions for the two problems are obtained through separation of variables. Another condition where the solution is obtainable by separation of variables is that of a well-stirred batch reactor, where a chemical species A is to be produced by the decomposition of another component B. The chapter shows that the batch reactor problem can also be solved by by Laplace transform.
