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)`

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

find the equation of the curve which passes through the point (2,2) and satisfies the differential equation y-x(dy)/(dx)=y^(2)+(dy)/(dx)

(x+2y^(3))(dy)/(dx)=y

The differential equations of all circle touching the x-axis at orgin is (a) (y^(2)-x^(2))=2xy((dy)/(dx)) (b) (x^(2)-y^(2))(dy)/(dx)=2xy ( c ) (x^(2)-y^(2))=2xy((dy)/(dx)) (d) None of these

The equation of the curve passing through (3,4) and satisfying the differential equation. y((dy)/(dx))^(2)+(x-y)(dy)/(dx)-x=0 can be

(dy)/(dx)=(x-y+3)/(2x-2y+5)

x(dy)/(dx)-y=2sqrt(y^(2)-x^(2))

dy/dx =(y)/(2y^3+x)

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