Plotting the derivative of a non symbolically defined function

I've solved a second order nonlinear differential equation in matlab and would like to plot it's derivative:

my attempts so far:

syms phi(t) 
figure 
hold on
for v =1:10
    [V] = odeToVectorField(diff(phi,2)== 28*(0.45-0.136)-(0.9)^2 * 0.45*1.21*sqrt(2)*v^2*sin(phi)*sin(pi/4-phi)/(4*0.25));
    M = matlabFunction(V,'vars', {'t','Y'});
    sol = ode45(M,[0 20],[0 5]);
    fplot(@(x)deval(sol,x,1), [0, 20])  
end
ddt = gradient(phi(:)) ./ gradient(t(:));
fplot(ddt)

Doing this returns an error. I've also tried

y =diff(phi)
fplot(y)

which just does nothing.

Any help would be great!

[VBBV]

Can you show the error ?

[Louis Sharma]

hi,

Error:

Error using symfun/subsref

Invalid argument at position 2. Symbolic function indexing evaluates the function at the input arguments. To perform colon indexing call FORMULA before indexing.

Answer 1

[Alan Stevens]

You could just do it totally numerically:

phi0 = 0;
dphidt0 = 5;
IC = [phi0 dphidt0];
tspan = 0:0.1:20;
v = 1:10;
phi = zeros(numel(tspan),numel(v));
dphidt =  zeros(numel(tspan),numel(v));

for i = 1:numel(v)
   
    [t, Y] = ode45(@(t,Y) odefn(t,Y,v(i)),tspan, IC);
    phi(:,i) = Y(:,1);
    dphidt(:,i) = Y(:,2);
    lgndstr = sprintf('v = %2i \n',i);
    lgnd(i,:) = lgndstr;
end
figure(1)
plot(t,phi),grid
xlabel('t'),ylabel('\phi');
legend(lgnd)

figure(2)
plot(t,dphidt),grid
xlabel('t'),ylabel('d\phi dt');
legend(lgnd)

function dYdt = odefn(~,Y,v)

        phi = Y(1);
        dphidt = Y(2);
        dYdt = [dphidt;
                28*(0.45-0.136)-(0.9)^2*0.45*1.21*sqrt(2)*v^2*sin(phi)*sin(pi/4-phi)/(4*0.25)];

end