This is Kit. I think your problem resembles the circuit of a Wien Bridge Oscillator with the exception that, in your case, all components are resistors, whereas the oscillator has some reactive components. Go to this link and you may find all your problems are solved.
http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=11&ved=0CDcQFjAAOAo&url=http%3A%2F%2Fnonlinear.eecs.berkeley.edu%2Fchaos%2Fintroduction_nonlinear_circuit_analysis.pdf&ei=FkRAT_mhEan9iQLln8SgAQ&usg=AFQjCNFBis5WULr2qNwHsepSsqTkF0uO3w&sig2=D1rtIasQ8rgdEfo8xC8_Gw
introduction_nonlinear_circuit_analysis.pdf
