General Chemical Reaction of Two Substances When two chemicals A and B react to produce substance X, the amount x of substance X is described by the DE dx/dt = k(a − x)m(b − x)n, a < b, where a and b represent the amounts of substances A and B, and m and n are positive integers.
(a) Describe the nature of the solutions of this equation for odd or even values of m and n by analyzing graphs of x′ versus x, thus determining the values of x for which the slope x′ is positive or negative. On this xx′ graph you can draw the phase line along the horizontal x-axis.
(b) Explain how different values of m and n affect the classification of equilibria. Which of the four odd/even exponent combinations gives a reasonable model if the manufacturing goal is to produce substance x?
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