Unknown parameters

This trick is also very handy if you want to examine the effect of different parameters on a differential equation.  So, let's consider a new equation (oh boy...):  [Graphics:../Images/index_gr_47.gif]

[Graphics:../Images/index_gr_48.gif]
[Graphics:../Images/index_gr_49.gif]
[Graphics:../Images/index_gr_50.gif]
[Graphics:../Images/index_gr_51.gif]
[Graphics:../Images/index_gr_52.gif]

(The [Graphics:../Images/index_gr_53.gif] is a useful trick to let Mathematica know that your k is a real number and simplify accordingly.  It doesn't actually matter in this particular problem, but sometimes it does...)

[Graphics:../Images/index_gr_54.gif]
[Graphics:../Images/index_gr_55.gif]
[Graphics:../Images/index_gr_56.gif]

[Graphics:../Images/index_gr_57.gif]

[Graphics:../Images/index_gr_58.gif]

Notice that I avoid [Graphics:../Images/index_gr_59.gif].  So, what if k is negative?

[Graphics:../Images/index_gr_60.gif]
[Graphics:../Images/index_gr_61.gif]
[Graphics:../Images/index_gr_62.gif]

[Graphics:../Images/index_gr_63.gif]

[Graphics:../Images/index_gr_64.gif]


Converted by Mathematica      July 20, 2003