In: Advanced Math
The questions below are about 2×2 autonomous systems of ODE. Parts (a) and (b) are unrelated. (a) Find the equilibrium solutions (critical points) of the system dx/dt = 2x−xy, dy/dt =−y+xy.(b) Consider the autonomous system dx/d t= −y+xy^3, dy/dt = x−x^3. The system has an isolated critical point at (x,y) = (1,1). Find the associated linear system at(1,1). Name and classify (as stable or unstable) the critical point of the linear system.