Question

3. Use you will receive no credit. he Laplace transform to solve f(t)ft). If you do not use the Laplace transform,

Answer 1

By Laplace transform

f^(t) = -4 F (t) ie f ' (t) + 4 f (t) = 0 taking Laplace transform L {f ' (t)} + 4 L {F (t)} = L{0} = 0 s F (s) - f (0) + 4 F (s) = 0 Here L {F (t)} = F (s) (s + 4) F (s) - F (0) = 0 F (s) = F (0)/s + 4, Here initial condition is not Given taking inverse Laplace L^- 1 {F (s)} = f (0) L^- 1 {1/s + 4} f (t) = f (0) e^- 4 t Because L^- 1 {1/s + a} e^- a t

Here initial condition is not given so will consider f(0) as a parameter

so solution will be of one parameter family