Applications of Linear Systems with Constant Coefficients 3975 y4321- 2 0. 4 0. 6 0. 8 1 1. 2 1. 4
F igure 9.7 The Path of an E lectron9.4 Mixture Problems
Many important problems in biology, chemistry, engineering, and physics
can be formulated within the following general framework. Suppose at a given
time t = 0 various containers (tanks, lakes, or rooms, for example) hold known
amounts of a certain substance. Also suppose at t ime t = 0 any or all of the
foll owing three events occur: A solution (fluid) containing a specified con-
centration of the substance begins to flow into one or more containers in the
system from outside the system. A solution begins to flow from one container
in the system to another container. A solution begins to flow out of the sys-
tem from some container. The mixture in each container is assumed to be
kept at a uniform, but not necessarily constant, concentration throughout by
a mixing device. T he problem is to determine t he amount of the substance
in each container as a function of time. For each problem of the type just
described, a system of differential equations to be solved is established using