Orthogonal trajectories of family of the curve `x^(2/3)+y^(2/3)=a^((2/3))` , where `a` is any arbitrary constant, is

Find the orthogonal trajectories of family of curves x^2+y^2=c x

Form the differential equation representing the family of curves given by (x - a)^(2) + 2y^(2) = a^(2) , where a is an arbitrary constant.

The differential equation for the family of curve x^2+y^2-2a y=0, where a is an arbitrary constant, is

From the differential equation of the family of circles (x -a)^(2) + (y - a)^(2) - a^(2) , where a is an arbitrary constant .

The differential equation of the family of curves y=e^(2x)(acosx+bsinx) , where a and b are arbitrary constants, is given by

The differential equation of the family of curves y=e^x(Acosx+Bsinx), where A and B are arbitrary constants is

Find the differential equation representing the family of curves y= ae^(bx+5) where a and b are arbitrary constants.

Differential equation of the family of curves v=A/r+B , where A and B are arbitrary constants, is

Each question contains statements given in two columns which have to be matched. Statements a,b,c,d in column I have to be matched with statements p,q,r,s in column II. If the correct matches are a-p, q-s, b-q, r c-p, q and d-s, then the correctly bubbled 4x4 matrix should be as follows: Figure Column I, Column II: Differential equation order 1, p.of all parabolas whose axis is the x-axis order 2, q.of family of curves y=a(x+a)^2, where a is an arbitrary constant degree 1, r. (1+3(dy)/(dx))^(2/3)=(4d^3y)/(dx^3) degree 3, s. of family of curve y^2=2c(x+sqrt(c)), where c >0

Consider the family of curves represented by the equation (x - h)^(2) + (y - k)^(2) = r^(2) where h and k are arbitrary constants . The differential equation of the above family is of curves -