You are telling it to produce two different plots because of two separate figure calls.
syms y(x) x Y
N=5;
r=0.05;
m=0.01;
p=1;
s=1;
t=0.1;
a=0.25;
b=0.25;
C0=1;
C=5;
t0= N+r+t*p*s-m;
t1=-(N+r+t*p*s-m);
Dy = diff(y);
D2y = diff(y,2);
ode = y-(1/x)*(N+r)-((t*p*s*Dy)/y)+((Dy*((s^2)-m))/y)+((D2y*x*(s^2))/(2*y));
[VF,Subs] = odeToVectorField(ode);
odefcn = matlabFunction(VF, 'Vars',{x,Y});
tspan = [C0 80];
ic = [t0 t1];
[x1,y1] = ode45(odefcn, tspan, ic);
figure
plot(x1, y1)
grid
hold on
syms y(x) x Y
f=(x+(x^2+4*r*x*(1-a-b))^0.5)/(2*(1-a-b));
t00=N/C;
t11=-N/(C^2);
Dy = diff(y);
D2y = diff(y,2);
ode2= y-((C-x+f*((1/(r+f))^(1/(1-a-b)))+t*p*s*x*Dy+x*Dy*((s^2)-m)+Dy*(C-x)+0.5*D2y*(x^2)*(s^2)-x*(s^2)*Dy)/x*(1+t*p*s-m));
[VF1,Subs1] = odeToVectorField(ode2);
odefcn1 = matlabFunction(VF1, 'Vars',{x,Y});
tspan2 = [C 1];
ic2 = [t00 t11];
[x2,y2] = ode45(odefcn1, tspan2, ic2);
figure
plot(x2, y2)
grid
hold off
figure % All Together 1!
plot(x1,y1(:,1), 'DisplayName','(x_1,y_1_1)')
hold on
plot(x1,y1(:,2), 'DisplayName','(x_1,y_1_2)')
plot(x2, y2(:,1), 'DisplayName','(x_2,y_2_1)')
plot(x2, y2(:,2), 'DisplayName','(x_2,y_2_2)')
hold off
grid
legend('Location','best')
figure % All Together 2!
yyaxis left
plot(x1,y1(:,1), 'DisplayName','(x_1,y_1_1)')
hold on
plot(x1,y1(:,2), 'DisplayName','(x_1,y_1_2)')
hold off
yyaxis right
plot(x2, y2(:,1), 'DisplayName','(x_2,y_2_1)')
hold on
plot(x2, y2(:,2), 'DisplayName','(x_2,y_2_2)')
hold off
grid
legend('Location','best')
The ‘x’ limits in the two integrations are not the same.
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