6. In this problem we explore bifurcations, that is, the changes in the phase line that result from small changes in the autonomous ODE. 2 (a) Sketch the phase line for y' = y sin(y) and state the nature of its equilibria. (b) Sketch the phase lines for y' = y sin(y) +0.1 and y = y sin(y) - 0.1 (a uniform small positive and small negative change, respectively, in the derivative). Discuss the effet of the small perturbations +0.1 on the equilibria. Note that you are being asked for a sketch, not a plot. There is no need for a plotting program. You know from earlier courses how the graph of a function (the right hand side) is changed when a constant value is added to the right hand side. (c) Consider the ODE y = y sin(y) +a where -0.2