Show the steps and explain the answer please

5. Find f(t) if f(t) - 2 / f(x) dx - 2t. Answer: Let L{f(t)} = F(s). Take the Laplace transform of both parts of the equation: 2 F($) - 2 - F(s) = 2-2 = F(s) F(s) - S s(s - 2) To invert F(s), one can use (a) partial fractions or (b) C / f(x) dx - F(s) o S 2 (a) F(s) = y (t ) = -1+ e2t s( S - 2 S 2 (b) S( S - 2) S L. F(s). Then CF (s) } - Ci 2 2 1 = 2 2t = f(t), and y (t) - ( f (x) dx - 2 / 2 dx = 2. 520 16 = e2t - 1