Answer
$a$ is a solution to the given problem.
Work Step by Step
We are given that $\dfrac{dy}{dx}=\dfrac{1}{x}$
$\dfrac{d}{dx}[\int_{1}^{x} \dfrac{1}{t} dt -3]=\dfrac{1}{x}$
This implies that
$y(1)=\int_{1}^{1} \dfrac{1}{t} dt -3=0-3=-3$
Thus, $a$ is a solution to the given problem.