9.1. Finding Singular Points
NOTE
Singular points occur when a coefficient in a particular differential equation becomes unbounded.
For example, in this differential equation
where
p(x) = Q(x)/P(x)
and
q(x) = R(x)/P(x)
the singular points occur where Q(x)/P(x) and/or R(x)/P(x) become unbounded.
In the following problems, you practice finding singular points in differential equations. But first, a quick example.
NOTE
EXAMPLE
Q. What are the singular points of this differential equation?
A. x1 = 2 and x2 = −2
First, put the equation into the following form:
where
p(x) = Q(x)/P(x)
and
q(x) = R(x)/P(x)
Doing so gives you
Therefore
and
Looks like p(x) and q(x) both become unbounded when 4 − x2 = 0, so the singular points are
x1 = 2 and x2 = −2
1. What are the singular points of this differential equation?
2. Solve for the singular points of this equation:
3. What are the singular ...
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