Find the orthagonal trajectories of the family of curves: y = x / (1 + kx). full

Question

Find the orthagonal trajectories of the family of curves: y = x / (1 + kx). full Question in the picture attached

Find the orthogonal trajectories of the family of curves: y = x/1+ kx (where k is an arbitrary constant). Please show clearly: (a) how to find a single differential equation that is satisfied by all the members of the given family; (b) how to obtain a differential equation satisfied by the orthogonal trajectories being sought; and (C) the solution of the differential equation obtained in (b).

Explanation / Answer

we are given     y= x/(1+kx)

so we will derivating both sides   we will get,

dy/dx = [(1+kx)(1) - (k)(x)]/(1+kx)

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