Engineering Board Exam Reviewer · Orthogonal Trajectories · medium

Find the orthogonal trajectories of the family y=Cex.

1. 2 x + y2 = K
2. - 2 x + y2 = K
3. x + 2 y2 = K
4. 2 x + y = K

Answer

A. 2 x + y2 = K

Solution

From y=Cex: dy/dx=Cex=y. Orthogonal family: dy/dx=- 1y. Then y,dy=-dx 2/2=-x+c y2+2x=K.

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