Find the orthoganal trajectories of the family. Use a graphing utility to graph several members of each family.
y = Ce^x
What am I supposed to do here? Can someone point me in the right direction?
express C as a function of x and y:
C = ye^-x
find y' implicitly
y'e^-x - ye^-x = 0
y' = y
so, for any point on the curve Ce^x, the slope is just y
On a perpendicular trajectory, the slope is -1/y
dy/dx = -1/y
y*dy = -dx
y^2/2 = -x+c
Thus parabolas opening to the left are orthogonal to the exponential curves.