V' = k

_{1}- k

_{2}V

^{2/3}, V(0) = V

_{0}> 0, k

_{1}> 0, k

_{2}> 0 ............................................................................................... (1)

(i) Verify that V

_{0}(t) = (k

_{1}/k

_{2})

^{3/2}is solution to differential equation (1).

(ii) If V(t) is the solution to differential equation (1), show that lim

_{t→∞}V(t) = V

_{0}(t) (geometry proof)

(iii) Prove it's useless to find an explicit formula for the solution to the DE (1) with initial condition V(0) =/= (k

_{1}/k

_{2})

^{3/2}.

(iv) Verify that

F(x) = arctanh (y

^{3}) + ln (y + 1) - ln (y - 1) + ln (y

^{2}+ y + 1)/2 - ln (y

^{2}- y + 1)/2 - 3y, y = x

^{1/3}

is primitive for f (x) = 1/(1 - x

^{2/3}) and analyze the equation F (x) - F (1) = t to solve x in function of t

PLEASE, I really need help.