#y=x-2y+xy^2#
#x=rcostheta#
#y=rsintheta#
Thus,
#rsintheta=rcostheta-2rcosthetaxxrsintheta+rcosthetaxx(rsintheta)^2#
#rsintheta=rcostheta-2r^2sinthetacostheta+r^2sin^2thetacostheta#
#rsintheta-rcostheta=r^2(-2sinthetacostheta+sin^2thetacostheta)#
#r(sintheta-costheta)=r^2sinthetacostheta(-2+costheta)#
#r(sintheta-costheta)+r^2sinthetacostheta(2-costheta)#
#r(sintheta-costheta+rsinthetacostheta(2-costheta))=0#
#r=0#
#sintheta-costheta+rsinthetacostheta(2-costheta)=0#
#rsinthetacostheta(2-costheta)=costheta-sintheta#
#r=(costheta-sintheta)/((2-costheta)sinthetacostheta)#