The differential equation of the family of curves whose equation is `(x-h)^2+(y-k)^2=a^2`, where `a` is a constant, is
(A) `[1+(dy/dx)^2]^3=a^2 (d^2y)/dx^2`
(B) `[1+(dy/dx)^2]^3=a^2 ((d^2y)/dx^2)^2`
(C) `[1+(dy/dx)]^3=a^2 ((d^2y)/dx^2)^2`
(D) none of these

[" The differential equation of the family of curves "],[y=c_(1)x^(3)+(c_(2))/(x)" where "c_(1)" and "c_(2)" are arbitrary "],[" constants,is "],[" O "x^(2)(d^(2)y)/(dx^(2))-x(dy)/(dx)-3y=0],[" (x) "(d^(2)y)/(dx^(2))+x(dy)/(dx)+3y=0],[" (x) "(d^(2)y)/(dx^(2))+x(dy)/(dx)-3y=0],[" (x) "(d^(2)y)/(dx^(2))-x(dy)/(dx)+3y=0]

If (d^(2)x)/(dy^(2)) ((dy)/(dx))^(3) + (d^(2) y)/(dx^(2)) = k , then k is equal to

What is the degree of the differential equation k(d^(2)y)/(dx^(2))=[1+((dy)/(dx))^(3)]^(3//2) , where k is a constant ?

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

Find the differential equation of the family of circles having a common centre (A) 2+(2y(d^(2)y))/(dx^(2))+2((dy)/(dx))^(2)+(2f)((d^(2)y))/(dx^(2))=0

The degree of the differential equation [1+("dy"/"dx")^2]^2=(d^2y)/(dx^2) is

If x^(2)+y^(2)=1 then (y'=(dy)/(dx),y''=(d^(2)y)/(dx^(2)))

if (x-a)^(2)+(y-b)^(2)=c^(2) then (1+((dy)/(dx))^(2))/((d^(2)y)/(dx^(2)))=?

y=x^(3)-4x^(2)+5 . Find (dy)/(dx) , (d^(2) y)/(dx^(2)) and (d^(3)y)/(dx^(3)) .

Find the order and degree of (d^3y)/dx^3+2((d^2y)/dx^2)^2-(dy)/(dx)+y=0