The solution of the differential equation  1+x2dydx+1+y2=0 is

If tan−1⁡y+tan−1⁡x=tan−1⁡C, thenddxtan−1⁡y+ddxtan−1⁡x=0⇒11+y2dydx+11+x2=0⇒1+x2dydx+11+y2=0Hence,tan−1⁡x+tan−1⁡y=tan−1⁡C is the solution of the given differential.