This problem i(t) is formed by the superposition of currents of two first-order circuits, so it contains two time constants.

The time constant of RL circuit is τ1= l/r = 2/4 = 0.5s..

iL(0)=2A

iL(∞)=20/4=5A

il(t)=5+(2-5)e^-t/τ=5+(2-5)e^-2t a

The time constant of RC circuit is τ 2 = RC = 2x0.1= 0.1s.

ic(0)=(20-8)/2=6A

ic(∞)=0A

ic(t)=6e^-t/τ=6e^- 10t A

i(t)=il(t)+ic(t)=5+(2-5)e^-2t+6e^- 10t a