plot 2D graph

Hi , I have 2 below Eq. :

diff(V,t) = V-V.^3/3-U+2;

diff(U,t) = 1.25*(V-U+0.9);

I want to plot U'-V' plot. I don't know how to do this.

can anybidy help me please.

thanks

[Walter Roberson]

It appears that you will need to work numerically, as the system is difficult to solve symbolically.

Answer 1

[Star Strider]

Try this:

syms t U(t) V(t) Y 
Eqs = [diff(V,t) == V-V.^3/3-U+2;  diff(U,t) == 1.25*(V-U+0.9)];
[VF,Sbs] = odeToVectorField(Eqs);
UVfcn = matlabFunction(VF, 'Vars',{t,Y});
Sbsc = sprintfc('%s',Sbs);

ic = [0; 0];
tv = linspace(0, 10, 5000);
[ts,UVs] = ode45(UVfcn, tv, ic);

figure
plot(ts, UVs)
grid

figure
plot(UVs(:,1), UVs(:,2))
grid
xlabel(Sbsc(1))
ylabel(Sbsc(2))

for k = 1:numel(ts)
    dUV(:,k) = UVfcn(ts(k),UVs(k,:));                   % Calculate Derivatives
end

figure
plot(dUV(:,1), dUV(:,2))
grid
lblf = @(x) sprintf('$\\frac{d%s}{dt}$',x);
xlabel(lblf(Sbsc{1}), 'Interpreter','latex')
ylabel(lblf(Sbsc{2}), 'Interpreter','latex')

I will let you explore it to discover how it works.