`(dy)/(dx)=2ytanhx`

yx (dy) / (dx) = a (y ^ (2) + (dy) / (dx))

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

If ax^(2)+2hxy+by^(2)+2gx+2fy+c=0, find (dy)/(dx) and (dx)/(dy) .Also,show that (dy)/(dx)(dx)/(dy)=1

If a x^2+2\ h x y+b y^2+2\ gx+2\ fy+c=0 , find (dy)/(dx) and (dx)/(dy) . Also, show that (dy)/(dx)dot(dx)/(dy)=1 .

The first integral of (dy)/(dx)((d^(2)y)/(dx^(2)))-x^(2)y((dy)/(dx))=xy^(2) will be

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

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