Find the differenital equation for the curve `y=k(x-k)^(2)` for all values of `k`.

Find the differential equation of the circles represented by y = k(x + k)^(2) where k is an arbitrary constant.

Find the differential equation from the equation (x-h)^(2)+(y-k)^(2)=a^(2) by eliminating h and k .

The order of the differential equation of the family of curves y=k_(1)2^(k_(2)x)+k_(3)3^(x+k_(4)) is (where, k_(1),k_(2), k_(3), k_(4) are arbitrary constants)

A normal is drawn at a point P(x,y) of a curve.It meets the x-axis at Q. If PQ has constant length k, then show that the differential equation describing such curves is y(dy)/(dx)=+-sqrt(k^(2)-y^(2)). Find the equation of such a curve passing through (0,k).

The differentiala equation representing the family of curves y^(2)=2k(x+sqrtk) where k is a positive parameter, is of

The differenital equation representing the family of curves y =a sin (lambdax +alpha) is :

Let a curve satisfying the differential equation y^(2)dx=(x-(1)/(y))dy=0 which passes through (1,1) if the curve also passes through (k,2) then value of k is

The area (in sq. units) of the region bounded by the curves y=2-x^(2) and y=|x| is k, then the value of 3k is

If K is constant such that xy + k = e ^(((x-1)^2)/(2)) satisfies the differential equation x . ( dy )/( dx) = (( x^2 - x-1) y+ (x-1) and y (1) =0 then find the value of K .