MEEN 221 Numerical Methods 1. A well-known coupled set of dimensionless differential equations (Lotka-Volterra equations) can be used to predict the population of predators and preys in a jungle These equations are given below: where x and y are the number of predators and preys respectively; and p, q, r and s are constants whose values can be taken as: p-1 ; q r $ 0.1 Use Euler forward method to solve the pair of ordinary differential equations (equations 1 and 2) for x and y from t-0 to t = 10. Use a step size of1-001 . Solve by MATLAB or EXCEL. Deliverables: 1. Method. Derive the discretized equations for equations 1 and 2 using Euler forward 2. Compute the solution for the first 20 time indices and complete the table below Index for time, i 0 20 3. Determine the solution for the time range t-0 to t-10 (time indices 0 to 100). Considering this time range:(i Plot both x and y versus time on the same plot, and on a second plot (ii) Plot y versus x. 4. From your plot in 3(i), at what time does the number of preys become the same as the number of predators? Note: If you solve by MATLAB, you must include your MATLAB script to the deliverables