Question

Consider the curves in the first quadrant that have equations y=Aexp(6x) where A is a positive constant. Different values of A give different curves. The curves form a family, F. A curve which at each of its points is perpendicular to the member of the family F that goes through that point is called an orthogonal trajectory to F. Each orthogonal trajectory to F satisfies the differential equation dy/dx = -1/ g(y) where g(y) = 6y. Find a function h(y) such that x=h(y) is the equation of the orthogonal trajectory to F that passes through the point P.