The general solution of the differential equation 1+x2+y2+x2y2+xydydx=0 is: (where C is a constant of integration)

The given differential equation 1+x2+y2+x2y2+xydydx=0Separate the variables 1+x21+y2+xydydx=01+x2xdx+y1+y2dy=01+x2xdx+1+y2=c Substitute 1+x2=t2 and 2xdx=2tdt and then integrate both sides ∫t2t2-1dt+1+y2=c∫t2-1t2-1+1t2-1+1+y2=ct+12logt-1t+1+1+y2=c1+x2+12log1+x2-11+x2+1+1+y2=c1+x2+1+y2=-12log1+x2-11+x2+1+c =12log1+x2+11+x2 -1+c