The differential equation of family of curves whose tangents form an angle of `pi/4` with the hyperbola `xy=k` is (A) `dy/dx=(x^2+ky)/(x^2-ky)` (B) `dy/dx=(x+k)/(x-k)` (C) `dy/dx=-k/x^2` (D) `dy/dx=(x^2-k)/(x^2+k)`

Which of the following is not the differential equation of family of curves whose tangent form an angle of (pi)/(4) with the hyperbola xy=c^(2)?(a)(dy)/(dx)=(x-y)/(x+y)(b)(dy)/(dx)=(x)/(x-y)(c)(dy)/(dx)=(x+y)/(x-y) (d)N.O.T.

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

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

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

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

a(x(dy)/(dx)+2y)=xy(dy)/(dx)

The differential equation of the family of curves y=k_(1)x^(2)+k_(2) is given by (where, k_(1) and k_(2) are arbitrary constants and y_(1)=(dy)/(dx), y_(2)=(d^(2)y)/(dx^(2)) )

x^2(dy/dx)^2-2xy dy/dx+2y^2-x^2=0

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

The differential equation satisfied by sqrt(1+x^2)+sqrt(1+y^2)=k(xsqrt(1+y^2)-ysqrt(1+x^2)), k in R is (A) dy/dx=(1+y^2)/(1+x^2) (B) dy/dx=(1+x^2)/(1+y^2) (C) dy/dx=(1+x^2)(1+y^2) (D) none of these