Question

Can someone help me out with this. I can't get my MATLAB to do these correctly, thanks!

Solve the following differential equations using the Matlab function "ode45”, ”ode23” or “ode 15s". For all cases use odeset to set the stats to on, so you can see the process for the solver. Plot your result. Use a legend on your plots. (a) y' =-2y y(0) = 5, tfinal = 2 (b) y" + 3 y' + 25 y = 0 y(0) = 10, y'(0) = 0, tfinal = 2 (c) y = ay - Oxy, x = -cx + yxy Where: y = the population of the prey x = the population of the preditor a = 1 = growth rate of the prey c = 0.75 = death rate of the preditor a=0.5 and y = 0.25 = effect of interaction of the two species y(0) = 2 and x(0) = 3, tfinal = 20

Answer 1

a)

- O X clear;clc; %d init = 5; tspan = 0:0.1:2; sol = ode 45 (@(t,y) -2*y, tspan, init); sol.stats plot (sol.x, sol.y) legend ('t vs y'); Figure 1 Eile Edit View & Insert Tools Desktop Window . Help IE - Homo -tvs y Command Window ans = struct with fields: nsteps: 11 nfailed: 0 nfevals: 67 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

b)

- O X II II III clear;clc; %d Figure 1 init = [10 0]; Eile Edit View tspan = 0:0.1:2; sol = ode 45 (@od, tspan, init); a dua sol.stats plot (sol.x, sol.y(1,:)) 12000 legend('t vs Y'); Insert Tools Desktop Window ORA Help 0 0 in it wnho o co vou awnn 0 10000 function dydt = od (t,y) dydt = zeros (2,1); dydt (1) = y(2); dydt (2) = -3*y (2) +25*y (1); end 8000 Command Window 6000 ans = struct with fields: 4000 nsteps: 19 nfailed: 0 nfevals: 115 2000 04 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

c)

- O X Figure 1 Eile Edit View Insert Tools Desktop Window Help dua kaka @ IE - о л ь о месо со н о п р о ме clear;clc; %d init = [32]; tspan = 0:0.01:20; sol = ode 45 (@od, tspan, init); sol.stats plot (sol.x, sol.y (1,:)) hold on plot (sol.x, sol.y (2,:)) legend('t vs x','t vs Y'); tvs x at vs y function dzdt = od (t, z) dzdt = zeros (2,1); dzdt (1) = -0.75*z (1) +0.25*z (1) *z (2); dzdt (2) = z (2) - 0.5*z (1) *z (2); Lend 16 - Command Window ans = struct with fields: nsteps: 21 nfailed: 2 nfevals: 139 fx >> 0 2 4 6 8 10 12 14 16 18 20