Posted by **Hannah** on Monday, March 5, 2012 at 10:43am.

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?

- Calculus -
**Steve**, Monday, March 5, 2012 at 1:11pm
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.

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