In Matlab you can design a set of loops where the parameters and the initial values can vary at a specific range. Then you just store the results or do an animation plot of the solutions. That's all in general, in practise it needs work.
A good start in answering this question is given in
W.C. Carter, Lecture 21: Higher-order ordinary differential equations HODEs, MIT, 2012:
http://pruffle.mit.edu/3.016/Lecture-21-twoside.pdf
Carter uses Mathematica (using Mathematica 7) for his solutions. A very helpful part of Carter's notes is that he has provided Mathematics notebooks with detailed code with comments. These notebook can be ported to a local copy of Mathematica for experiments. Another good place for a discussion about simulating HODEs is given in
http://mathforum.org/kb/search!execute.jspa?q=numerate&forumID=79&rankBy=9&start=105
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