Answer
$$y=-3e^{3x-6}+4.$$
Work Step by Step
By separation of variables, we have
$$\frac{dy}{3y-12}=dx$$
Then by integration, we get
$$\ln(3y-12)=3x+c\Longrightarrow y=\frac{1}{3}(Ae^{3x}+12).$$
Now, since $y(2)=1$, then $1=\frac{1}{3}(Ae^{6}+12)\Longrightarrow A=-9e^{-6}$. So the general solution is given by $$y=-3e^{3x-6}+4.$$
