Calculus
posted by Hannah on .
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.