confusion in time invariance?
The given system is not time invariant due to the term $\cos(\pi t / 3)$.

Given a system definition of the form:

$$y(t) = 3 x(t) + \cos( \pi t/3) $$ it's easy to see that

$$ y(t-d) = 3 x(t-d) + \cos(\pi (t-d) /3) \neq T\{x(t-d)\} = 3 x(t-d) + \cos(\pi t/3)$$

hence the system is time varying...