I know this is probably a super easy problem, but I'm not getting it.
For problems 15-20, find the equation of the orthogonal trajectories to the given family of curves.
I used implicit differentiation and I got dy/dx=-x/4y
I know the slope of the orthagonal trajectory curve will be dy/dx=-1/f(x,y) which is dy/dx=4y/x
integrating that equation gave me y=x4+k but the answer in the back of my textbook is y=kx4
not sure why the constant is in the wrong place