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function dy=eq3(t,y) dy=zeros(2,1); dy(1)=20*(10+20*cos(t)-y(1))/sqrt((10+20*cos(t)-y(1))^2+(20+15*sin(t)-y(2))^2); dy(2)=20*(20+15*sin(t)-y(2))/sqrt((10+20*cos(t)-y(1))^2+(20+15*sin(t)-y(2))^2);

[t1,x]=ode45('shier1',[0 15],[25 2]); [t2,y]=ode45('shier2',[0 15],[25 2]); x1=x(:,1);x2=x(:,2); x3=x2./(x1+x2); y1=y(:,1);y2=y(:,2); y3=y2./(y1+y2);

[T,Y]=ode45('rigid',[0 12],[0 1 1]); plot(T,Y(:,1),'-',T,Y(:,2),'*',T,Y(:,3),'+')

function dy=eq4(t,y) dy=zeros(2,1); dy(1)=5*(10+20*cos(t)-y(1))/sqrt((10+20*cos(t)-y(1))^2+(20+15*sin(t)-y(2))^2); dy(2)=5*(20+15*sin(t)-y(2))/sqrt((10+20*cos(t)-y(1))^2+(20+15*sin(t)-y(2))^2);

[x,y,z]=dsolve('Dx=2*x-3*y+3*z','Dy=4*x-5*y+3*z','Dz=4*x-4*y+2*z','t'); x=simple(x) y=simple(y) z=simple(z)

[T,Y]=ode15s('vdp1000',[0 3000],[2 0]); plot(T,Y(:,1),'-')

t0=0,tf=2; [t,y]=ode45('eq2',[t0 tf],[0 0]); X=1; Y=0:0.01:2; plot(X,Y,'-') hold on plot(y(:,1),y(:,2),'*')

function dy=rigid(t,y) dy=zeros(3,1); dy(1)=y(2)*y(3); dy(2)=-y(1)*y(3); dy(3)=-0.51*y(1)*y(2);

function dx=shier(t,x) dx=zeros(2,1); dx(1)=x(1)*(1-0.1*x(2)); dx(2)=x(2)*(-0.5+0.02*x(1));

clear x=0:0.01:1; y=-5*(1-x).^(4/5)/8+5*(1-x).^(6/5)/12+5/24; plot(x,y,'*')