`(dy)/(dx)=(1+x^(2))/(1+y^(2))`

(dy)/(dx)=(1+y^(2))/(1+x^(2))

Solve: (dy)/(dx)=(1+y^(2))/(1+x^(2))

Solve: (dy)/(dx)=(1-x+x^(2))/(1-y-y^(2))

General solution, of (dx)/(dy)+(1+x^(2))/(1+y^(2))=0 is

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

(y-x(dy)/(dx))=3(1-x^(2)(dy)/(dx))

Order and degree of (dy)/(dx)=(x^((1)/(2)))/(y^((1)/(2))(1+x^((1)/(2)))) are 1 and 1.