I'd wonder if anyone can help me set up these differential equations. I don't know how to experss an derivative of a function calculated at certain point in a differential equation in Mathematica.
Thanks.
Perhaps start with the documentaiton for DSolve
http://reference.wolfram.com/language/ref/DSolve.html
or NDSolve
http://reference.wolfram.com/language/ref/NDSolve.html