advanced mathematics

A single-plate absorption column (see section 1.22 ) is described by the following equation: hddx=Lxf+GyfLxGy where x and y are mole fractions of the solute in the liquid and gas phases, respectively, is time, h is the liquid holdup, and L and G are the liquid and gas flow rates, respectively. The quantities h,L,G,xf, and yf are prescribed constants, with the last two representing compositions of the two feed streams. Furthermore, let the equilibrium relation be y=1+(1)xx where >0 is the constant relative volatility. Determine the number of steady states and their stability character