Problem 11 (Finding critical points). Find the critical points of the following nonlinear system. x' = x^2 - xy y' = 4xy + y^2 - 2y. Problem 12 (Solving nonlinear system). Given the system of nonlinear ODE x= xy - 6x y' = xy - 2x + y - 2. Linearize the above about its critical point (0,2) and classify its type and stability.
Show transcribed image textProblem 11 (Finding critical points). Find the critical points of the following nonlinear system. x' = x^2 - xy y' = 4xy + y^2 - 2y. Problem 12 (Solving nonlinear system). Given the system of nonlinear ODE x= xy - 6x y' = xy - 2x + y - 2. Linearize the above about its critical point (0,2) and classify its type and stability.