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Math 331, Fall 2004: Problem Set 5. Due Oct18
- Find all the solutions to the differential equation
Among them, single out the one for which .
[Hint: read the help page for
dsolve, or just do it in your
head. It is that easy.]
- Consider the first order system
- a Find the fixed points.
- b Determine the 'shape" of the solutions around the fixed point (that is, study whether it is a saddle, a source, a spiral source, a sink, a spiral sink or a center)
- c Determine whether
a solution of the system. Justify your answer.
- (no Maple)Consider a linear system , where is a real 2x2 matrix. Show that if
and
are two solutions and and are two real numbers, then
is also a solution.
- Find all the fixed points of the system
a fixed point being a solution for which both and
stay constant. For each of these points, describe the behavior of the
solutions that have initial conditions nearby. You can use Maple to
figure out what happens for nearby points, or you can use more
mathematical methods.
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Moira Chas
2004-10-19