Solve the following differential equation y2 x2 dx 2xydy 0 ........

Explanation:

(y²  -x²)dx-2xydy  =0

dy/dx  =y²  -x²  /2xy

let y=vx

dy/dx  =v+  xdv/dx

v +x dv/dx  =1/2  (v-  1/v)

x dv/dx  =1/2  (v²  -1/v) –v

x dv/dx   =  -[v²   +1]/2v

2v dv/1+v²  = -dx/x

Integrating both side

Log (1+v²)  =-logx  +c

Log (1+v²)  =log(c1/x)

1+v²  =  c1/x

Y=vx

1+(y/x)²  =c/x

X²  +  y²   =cx

(x- c/2)²  +  y²  =c²/4