Recently my controls teacher gave me a problem set. In it he asks us to linearize the following equation: y* = y - y^3 +u (y* is the first derivative of y) about the point y+=1. I found the solution was to take the partial derivative of f(y) where f(y) = y - y^3 evaluated at y+ and to multiply it by the change in y. I then found its transfer function to be: 1/(s+2).
A similar problem is with the equation: y** +3y* +2y = x^3 about the point x+ = 0. I am not sure how to do the problem but my guess is that I will take two partials of x^3 evaluated at x+ and find the transfer function from there. Am I way off the mark here? Do I need to do anything about the 2y term?