Consider the following ordinary differential equation x′′+x′+x2−x=0. (i) What is the order of equation (2)? Using y=x′ rewrite equation (2) as a system of two first order ordinary differential equations. [5 Marks] (ii) Calculate all steady states of the system. [10 Marks] (iii) Show that the Jacobian of the system is J(x,y)=[01−2x1−1]. Calculate the eigenvalues of the Jacobian at each steady state and use these to characterise the stability of each steady state.
