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The solution of the differential equation (x^2+y^2)dx=2xydy is
Dear pallavi
(x^2+y^2)dx=2xydy
dy/dx = (x2+y2)/2xy
let y=vx
so dy/dx = v + xdv/dx
put these value
v + xdv/dx = (x2+(xv)2)/2xvx
v + xdv/dx =(1+v2)/2v
x dv/dx = (1+v2)/2v -v
x dv/dx = (1- v2)/2v
2v/(1- v2) dv = dx/x
now let 1-v2 =t
-2vdv =dt
-dt/t =dx/x
-lnt = lnx + C
where C is constant
t =c/x
or 1-v2 =C/x
or 1-(y/x)2 =C/x
(y/x)2 =1 -C/x
y2 = x2 -Cx
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