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

The solutions of y=x((dy)/(dx)+((dy)/(dx))^(3)) are given by (where p=(dy)/(dx) and k is constant )

x(dy)/(dx)=y

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

The solution of y^2=2y(dy)/(dx)-((dy)/(dx))^(2), is

Find the order and degree y=x((dy)/(dx))+((dy)/(dx))-((dy)/(dx))^(3)

Order and degree of the differential equation y(dy)/(dx)=(x)/((dy)/(dx) + ((dy)/(dx))^(3)) respectively are

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

A solution of y=2x((dy)/(dx))+x^(2)((dy)/(dx))^(4) is