Please solve the entire question and I will surely upvote.

2. Consider a process that uses bacteria to produce antibiotic. The reactor is contaminated with protozoan that consumes bacteria. Assume that predator - prey equations are used to model the system ( x I : bacteria (prey), 22 : protozoa (predator). The time unit is in days. dtdx1=x1x12dtdx2=x122 (i) What are the trivial and nontrivial steady state concentration x/s,x2s ? (ii) Use the nontrivial steady state values of xl and x2 to scale the variables as yl=x/xl s and y2=x2/x2 s and derive the governing equations in terms of scaled variables y1 an y 2. (iii) Linearize the scaled equations and write in state space form. Find the eigen values of the Jacobian around the nontrivial steady state (i.e y/s=1,y2s=1 ) in terms of and (iv) Evaluate the eigen values for ==1. Discuss about the stability of the nontrivial steady state. What type of phase plane plot (y1 vs y 2 ) do you expect? (v) Discuss about the stability of the trivial steady state. (vi) For ==1 and initial conditions yl (0)=1.05 and y 2(0)=0.95 use explicit Euler to find y1 versus t and y2 versus t