tangency and the origin `(x-y)dy=(x+y+1)dx`

Which one of the following differential equations represents the family of straight lines which are at unit distance from the origin a) (y-x(dy)/(dx))^2=1-((dy)/(dx))^2 b) (y+x(dy)/(dx))^2=1+((dy)/(dx))^2 c)(y-x(dy)/(dx))^2=1+((dy)/(dx))^2 d) (y+x(dy)/(dx))^2=1-((dy)/(dx))^2

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

Express (1+e^(x//y)) dx+e^(x//y) (1-(x)/(y)) dy=0 in the form (dx)/(dy) = F((x)/(y)) .

Solve: x dx+y dy=x dy-y dx

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

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

Solve the following differential equations (i) (1+y^(2))dx = (tan^(-1)y - x)dy (ii) (x+2y^(3))(dy)/(dx) = y (x-(1)/(y))(dy)/(dx) + y^(2) = 0 (iv) (dy)/(dx)(x^(2)y^(3)+xy) = 1

The differential equation of all circles passing through the origin and having their centres on the x-axis is (1) x^2=""y^2+""x y(dy)/(dx) (2) x^2=""y^2+"3"x y(dy)/(dx) (3) y^2=x^2""+"2"x y(dy)/(dx) (4) y^2=x^2""-"2"x y(dy)/(dx)