The solution of the differential equation $\frac{dy}{dx}=-\frac{x}{y}$ is :

$x^2+y^2=2C,$ where C is constant of integration. $x-y^2=2C,$ where C is constant of integration. $x^2+y=2C,$ where C is constant of integration. $x^2-y^2=2C,$ where C is constant of integration.

$x^2+y^2=2C,$ where C is constant of integration.

The correct answer is Option (1) → $x^2+y^2=2C,$ where C is constant of integration. $\frac{dy}{dx}=-\frac{x}{y}$ so $\int ydy=\int -xdx$ $\frac{y^2}{2}=-\frac{x^2}{2}+C$ so $x^2+y^2=2C$