unknowns multiplied together is, in a sense, a power 2 of unknowns); and they won’t
be inside another function (such as a sine).
But a nonlinear equation is much different, allowing for powers of 2(y' y^2 ), mul-
tiplying differences (yy' x); and even being inside another function (y' xsin y).
Thus, the nonlinear equations are not as easy to solve as linear differential equations.
But that does not mean they lack importance. In fact, because nonlinear equations are
more realistic in describing real-life problems, they are much more interesting (and
challenging) to mathematical and scientific researchers in many fields.VECTOR AND OTHER ANALYSES
What is a vector?
A vector is considered to be an element of a linear or vector space. A vector is different
than a point, as it represents the displacement between two points, not the physical loca-
tion of a point in space. Vectors also define a direction; points do not. Vectors are usually
represented by a line segment in a specific direction on a graph, with an arrow at one end
of the segment. They can also be represented in several ways, including bold letters in an
equation, for example, vectors Aand B, and with arrows above the vector, such as x><.What is the componentof a vector?
A component of a vector is one with nnumbers in a certain order. It is usually listed as
(x 1 , x 2 , ..., xn), in which the numbers within the parentheses are called the compo-
nents of the vector x><.
Logically, an infinite number of vectors can have the same components. For
236 example, if the components are [3, 4], we know there are an infinite number of pairs of
Rabbit populations are affected not only by birth rates, but also by factors such as predation, disease, and avail-
able food supplies. Systems of differential equations may be used to take all these elements into consideration
and estimate actual population numbers. The Image Bank/Getty Images.