General solution of differential equation : $(1-x^2)(1-y)dx -xy (1+y) dy=0$

Question

$(a)\;x^2+2 \log x =(y+1)^2+6(y+1) +4 \log (y+1) +c \\ (b)\;\frac{x^2}{2}- \log x =\frac{(y-1)^2}{2}+3(y-1) +2 \log (y-1) +c \\ (c)\;\frac{x^2}{2}+\log x =\frac{(y+1)^2}{2}+3(y-1) +2 \log (y+1) +c \\ (d)\;\frac{x^2}{2}+ \log x =\frac{(y-1)^2}{2}+3(y-1) +2 \log (y-1) +c$