Calculus

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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 -

    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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