MATLAB: Can anyone check the code for ode45 function question

Question

function dz=f2(t,z)
dz=[z(1)-z(2)^2*z(1)-z(2); z(1)];
 
t=[0 20];
initz=[1; 1];
[t,z]=ode45(@f2, t, initz);
plot(t, z(:,2))

Is my solution correct?

Answer 1

Just noticed it you need to reduce your second order to first order to ode as below:

syms y(t)
ode1=diff(y,2) == 1-y^2;
ode2=diff(y,1) == y;
 
vars = y(t)
V = odeToVectorField([ode1,ode2])
M = matlabFunction(V,'vars', {'t','Y'})
interval = [0 5];  %time interval
y0 = [1 1];      %initial conditions
ySol = ode45(M,interval,y0);
tValues = linspace(interval(1),interval(2));
yValues = deval(ySol,tValues,1); %number 1 denotes first solution likewise you can mention 2 solution
plot(tValues,yValues,'-')
figure
yValues = deval(ySol,tValues,2);
plot(tValues,yValues,'-or')