# [Recommended]MATLAB Work

MATLAB Work function ex_with_param t0=0; tf=3; y0=1; a=1; [t,y]=ode45(@f,[t0,tf],y0,[],a); disp([‘y(‘,num2str(t(end)),’) = ‘,num2str(y(end))]) disp([‘length of y =’, num2str(length(y))]) %————————————————- function dydt=f(t,y,a) dydt=-a*(y-exp(-t))-exp(-t); function ex_with_2eqs t0 =…

MATLAB Work
function ex_with_param
t0=0; tf=3; y0=1;
a=1;
[t,y]=ode45(@f,[t0,tf],y0,[],a);
disp([‘y(‘,num2str(t(end)),’) = ‘,num2str(y(end))])
disp([‘length of y =’, num2str(length(y))])
%————————————————-
function dydt=f(t,y,a)
dydt=-a*(y-exp(-t))-exp(-t);
function ex_with_2eqs
t0 = 0; tf = 20; y0 = [10;60];
a = .8; b = .01; c = .6; d = .1;
[t,y] = ode45(@f,[t0,tf],y0,[],a,b,c,d);
u1 = y(:,1); u2 = y(:,2); % y in output has 2 columns corresponding to u1 and u2
figure(1);
subplot(2,1,1); plot(t,u1,’b-+’); ylabel(‘u1’);
subplot(2,1,2); plot(t,u2,’ro-‘); ylabel(‘u2’);
figure(2)
plot(u1,u2); axis square; xlabel(‘u_1’); ylabel(‘u_2’); % plot the phase plot
end
%———————————————————————-
function dydt = f(t,y,a,b,c,d)
u1 = y(1); u2 = y(2);
dydt = [ a*u1-b*u1*u2 ; -c*u2+d*u1*u2 ];
end
attachment
MAT275_LAB04_v2.pdf

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