I was wondering if anyone knows how to cause the DSolve function to critically damp (i.e. b^2 = 4ac). It is a symbolic problem, and so I cannot even have numbers in it to tell it that.
My problem: m*y'' + b*y' + k*y + mg = 0
All of it has to be left in symbols, and it involves damping a spring. I just don't know how to make mathematica do it.
Any comments and suggestions on this problem would be greatly appreciated.