The orthogonal trajectories of the family of curves `y=Cx^(2)`, (C is an arbitrary constant), is

Find the orthogonal trajectories of xy = c

The orthogonal trajectories of the circle x^(2)+y^(2)-ay=0 , (where a is a parameter), is

If the differential equation of the family of curve given by y=Ax+Be^(2x), where A and B are arbitary constants is of the form (1-2x)(d)/(dx)((dy)/(dx)+ly)+k((dy)/(dx)+ly)=0, then the ordered pair (k,l) is

The equation to the orthogonal trajectories of the system of parabolas y=ax^2 is

Form the differential equation representing the family of curves y = a sin ( x + b) , where a, b are arbitrary constants.

In each of the Exercises 1 to 5, form a differential equation representing the given family of curves by eliminating arbitrary constants a and b. 1. (x)/(a) + (y)/(b) = 1

The differential equation which represents the family of curves y=c_(1)e^(c_(2^(x) where c_(1)andc_(2) are arbitary constants is

The differential equation corresponding to the family of curves y=e^x (ax+ b) is

The value of k such that the family of parabolas y=cx^(2)+k is the orthogonal trajectory of the family of ellipse x^(2)+2y^(2)-y=c, is

The differential equation representing all possible curves that cut each member of the family of circles x^(2)+y^(2)-2Cx=0 (C is a parameter) at right angle, is