We return to he equation to see two variations on how to obtain numerical solutions for it. In the first one, we can supply a vector of time nodes and receive the solution at exactly those times.

f = @(t,u) sin( (t+u).^2 );

t = linspace(0,4,60)';

[t,u] = ode45(f,t,-1);

plot(t,u,'.')

xlabel('t'), ylabel('u(t)'), title('Solution at 60 points') % ignore this line

In the second variation, we see that it's also possible to create a callable function for the solution. Essentially this is a high-quality interpolant of the computed particular values.

u = @(t) deval( ode45(f,[0,4],-1), t );

fplot(u,[0,4])

xlabel('t'), ylabel('u(t)'), title('Solution as a callable function') % ignore this line