Consider the following system of linear ODEs: x(t)=yx2+1y(t)=yx2+1 where x and y are both functions of t. Part a) Draw a vector field for this system of ODEs in the xy-plane with the following additional elements 1. A curve representing where x=0 2. A curve representing where y=0 3. A star at each of the fixed points The above elements should be consistent with your vector field. Feel free to use computer software to assist you in drawing your vector field. WolframAlpha is a very good resource for this. Part b) Using your diagram, identify which of your fixed points are stable, unstable, or saddle points. Also identify if the fixed points are oscillatory or not. Part c) Calculate the positions of your fixed points. Part d) Find the Jacobian of the system of ODEs at each of the fixed points. Consider the following system of linear ODEs: x(t)=yx2+1y(t)=yx2+1 where x and y are both functions of t. Part a) Draw a vector field for this system of ODEs in the xy-plane with the following additional elements 1. A curve representing where x=0 2. A curve representing where y=0 3. A star at each of the fixed points The above elements should be consistent with your vector field. Feel free to use computer software to assist you in drawing your vector field. WolframAlpha is a very good resource for this. Part b) Using your diagram, identify which of your fixed points are stable, unstable, or saddle points. Also identify if the fixed points are oscillatory or not. Part c) Calculate the positions of your fixed points. Part d) Find the Jacobian of the system of ODEs at each of the fixed points