the functions x(t) and y(t) satisfy:
y' =-3y + xy
a) show that the solution trajectories in x,y phase space are given by
ln|(x^3)y| = x +2y + constant
b) determine the critical points of the system. solve the linear comparison system corresponding to each critical point(i.e. determine a relationship between x and y (or between u and v for the translated critical points)) - determine the type and stability of each critical point, and sketch the trajectories in the vicinity of each.
i would be sooo grateful if someone could please help me with this!!
honestly, i'm lost, and any help would be much appreciated