plotting 4 variables in the same graph

i need to plot this function with 4 variables t,s,a,b

format long
p=pi ; 
a=0 ;
b=0 ;
syms y(t)
for a=0:10 ;
    for b=0:10;
       [V] = odeToVectorField(diff(y, 2) == -1*(a-b*cos(2*t))*y);
M = matlabFunction(V,'vars', {'t','Y'});
sol = ode45(M,[0 2*pi],[0 1]);
    end
end
 sol.y
 fplot(@(x)deval(sol,x,1),[0, 20])

Answer 1

[Star Strider]

I have no idea what ‘s’ is, since it only appears in your question, not in your code.

Try this:

syms y(t) t Y a b 
[V,Subs] = odeToVectorField(diff(y, 2) == -1*(a-b*cos(2*t))*y);
M = matlabFunction(V,'Vars',{t,Y,a, b});

tspan = linspace(0, 2*pi, 75);
av = 0:10;
bv = 0:10;
for k1 = 1:numel(av)
    for k2 = 1:numel(bv)
        [t,y] = ode45(@(t,Y)M(t,Y,av(k1),bv(k2)),tspan,[0 1]);
        yc{k1,k2} = y;
    end
end

figure
hold on
for k1 = 1:11
    for k2 = 1:11
        plot(t,yc{k1,k2})
    end
end
hold off
grid

I leave identifying the various curves to you. (There would be 121 different plots. Consider 11 different figures, with the 11 sets of curves either plotted on the same axes or with 11 subplots. The choice is yours.)

EDIT — (25 Jul 2020 at 23:56)

Corrected typographical error.