A skydiver's position is given by x(t) and is accelerating at the rate x''(t). By Newton's second law, we can infer mx''(t)=a(t)x'(t), where a(t)=1/(t+1) is a function describing the air resistance and m=2 is the skydiver's mass.

a) Find the general solution of this equation, for t is bigger or equal to 0. Hint: can you solve for v=x' first?

b) Find all solutions x(t) satisfying x(0) =2000.