Use Butterworth and Chebychev filters I need to calculate frequency response, phase response and apply to signals the Butterworth, Chebychev1 and Chebychev2 band-pass filters.

I'm developing in C++ with Qt, and I'm looking for algorithms or a (free) library to do that. I have my plotting solution, I just need the formulas.

The input values I have are the time/amplitude signal, the order of the filter and the low and high cut-off frequencies.
You might try Vincent Falco's Collection of Useful C++ Classes for Digital Signal Processing.

The StackOverflow Question A C++ library for IIR filter offers a few more suggestions.

Finally: the hard part for Butterworth/Chebychev filters is really the design, not the implementation.  You might consider doing the design in Matlab (or Gnu Octave), or an online site like: http://www-users.cs.york.ac.uk/~fisher/mkfilter/.  Writing the C code should be trivial once you know the coefficients for the recurrence relation.