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