" 16."(dy)/(dx)+(y(y-1))/(x(x-1))=0

(dy)/(dx)+(y(y-1))/((x-1))=0

(dy)/(dx) of (x^(y))(y^(x))=1

The family of curves represented by (dy)/(dx)=(x^(2)+x+1)/(y^(2)+y+1) and the family represented by (dy)/(dx)+(y^(2)+y+1)/(x^(2)+x+1)=0

The family of curves represented by (dy)/(dx)=(x^(2)+x+1)/(y^(2)+y+1) and the family represented by (dy)/(dx)+(y^(2)+y+1)/(x^(2)+x+1)=0

The family of curves represented by (dy)/(dx)=(x^(2)+x+1)/(y^(2)+y+1) and the family represented by (dy)/(dx)+(y^(2)+y+1)/(x^(2)+x+1)=0

If e^x+e^y=e^(x+y) , prove that (dy)/(dx)=-(e^x(e^y-1))/(e^y(e^x-1)) or, (dy)/(dx)+e^(y-x)=0

If xsqrt(1 + y) + ysqrt(1 + x) = 0 x != y prove that (dy)/(dx) = (-1)/((1 + x)^(2))

If xsqrt(1 + y) + ysqrt(1 + x) = 0 x != y prove that (dy)/(dx) = (-1)/((1 + x)^(2))

If e^(x) + e^(y) = e^(x + y) , then prove that (dy)/(dx) = (e^(x)(e^(y) - 1))/(e^(y)(e^(x) - 1)) or (dy)/(dx) + e^(y - x) = 0 .