Page 30 - Schaum's Outline of Differential Equations
P. 30
CHAP. 2] AN INTRODUCTION TO MODELING AND QUALITATIVE METHODS 13
2.20. Assume a chemical compound, X, is such that its rate of decay is proportional to the cube of its difference from a
given amount, M, where both X and M are given in grams and time is measured in hours. Model this relationship
with a differential equation.
2.21. Suppose A and B are two vats interconnected with a number of pipes and drains. If A(t) and B(t) represent the number
of gallons of liquid sugar in the respective vats at time t (hours), what do A'(t) and B'(t) represent?
2.22. Consider Problem 2.21. Suppose the following system of differential equations models the mixing of the vats:
where a, b, c, d, e, and/are constants. What is happening to the liquid sugar and what are the units of the six constants?
