Answer
$$ y= 1000 e^{3t-6}.$$
Work Step by Step
The solution of the differential equation is given by $$ y=Ce^{3t}.$$ To find $ C $, we use the initial condition $ y(2)=1000$, then we have $ C=1000 e^{-6}$. Hence the solution is $$ y=1000 e^{-6}e^{3t}=1000 e^{3t-6}.$$
