The solution of dydx=x2+y2+12xy satisfying y(1)=1 is given by

dydx=x2+y2+12xy 2xy dy=x2+y2+1dx2xydy-y2dx=x2+1dx∫2xydy-y2dxx2=∫1+1x2dx→∫dy2/x=x−1x+c→y2x=x−1x+c→y2=x2−1+cx   passes through⁡(1,1)1=cy2=x2−1+x