A researcher is studying the growth of a bioluminescent organism. The volume VVV of the organism (in mm3\text{mm}^3mm3) satisfies the differential equation
dVdt=6t2lntV \frac{\text{d}V}{\text{d}t} = \frac{6t^2 \ln t}{V} dtdV=V6t2lntfor t≥1t \ge 1t≥1, where ttt is the time in days since the start of the observation.
Given that the volume of the organism is 4 mm34\text{ mm}^34 mm3 when t=1t = 1t=1, solve the differential equation to find an expression for V2V^2V2 in terms of ttt.
