Answer
True
Work Step by Step
True.
The slope of the curve at $(3,1)$ is given by $y'(3)$.
Substituting the point $(x,y)=(3,1)$ into the differential equation,
$(2\cdot 3-1)y'(1)=3+2\cdot 1$
$5y'(1)=5$
$y'(1)=1$
Thus, that the slope of the curve at $(3,1)$ is 1 is true.