a. Explain how you know that there exists a unique solution of the 1UP d (1? = 2 t yg, gag} = ya for every 1C [tn5 y\") in the plane. d b. Solve the IVP dE: = 2: y? , mm = yo , and state any equilibrium solutions. c. Show that, for the solutions in part b., (i) every solution is symmetric about the yaxis; (ii) if ya :15 III, the solution has a nite domain of validity bounded by two vertical asymptotes; (iii) if ya r: 0, the solution is a negative function dened for all real I, and is asymptotic to an equilibrium solution as |t| > oo which separates these solutions from those in part [ii]. d. Illustrate how the solutions depend on the initial condition y\" by plotting the solutions for ya = D.l]1, l], l].1 . (Use Maple le MMTABplots if you wish.) Does the solution depend continuously on the [Us (i.e.J do two solutions with nearby ICs stay nearby)?r Explain your reasoning