Answer
$x^2+y^2=K$
Work Step by Step
Write the differential equation as follows: $-\dfrac{dx}{dy}=\dfrac{y}{x}$
or, $ -x \ dx =y \ dy$
$-\int x dx=\int y dy$
or, $\dfrac{y^2}{2}+C= -\dfrac{x^2}{2}$
or, $ \dfrac{-x^2-y^2}{2}=C$
or $ x^2+y^2=-2C$
or, $x^2+y^2=K$
