Answer
$\dfrac{y^2}{2}=\dfrac{x^2}{2}+C$
Work Step by Step
We are given that $\dfrac{dy}{dx}=\dfrac{x}{y}$
We will separate the variables to obtain:
$y \ dy=x \ dx$
Integrate to obtain:
$\int y \ dy=\int x \ dx$
This implies that $\dfrac{y^2}{2}=\dfrac{x^2}{2}+C$
