v(t) is the potential difference across which nodes?
The *circuit has a time constant of R.C The switch is perhaps there to mislead you.
Since it's homework I'll leave you to calculate R. What's the value of X btw ? You may need to include that in your answer.
V(t) is easily calculated if you've been following your lectures. It'll help somewhat if you simplify the circuit using Norton's or Thevenin's theorem.