The rate of change of the concentration C C\,C of a chemical reagent in a reaction is modeled by the differential equation
dCdt=8tlntC,t>0 \frac{\text{d}C}{\text{d}t} = \frac{8t \ln t}{C}, \quad t > 0 dtdC=C8tlnt,t>0where t t\,t is the time in seconds. Given that the concentration is 6 units when t=1t = 1t=1, solve the differential equation to find an expression for the concentration at any time ttt, giving your answer in the form C2=f(t)C^2 = f(t)C2=f(t).
