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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Orthogonal trajectories Two curves are orthogonal to each
other if their tangent lines are perpendicular at each point of intersection (recall that two lines are perpendicular to each other if their
slopes are negative reciprocals). A family of curves forms orthogonal
trajectories with another family of curves if each curve in one family is
orthogonal to each curve in the other family. For example, the parabolas y = cx²
form orthogonal trajectories with the family of ellipses
x² + 2y² = k, where c and k are constants (see figure).
Find dy/dx for each equation of the following pairs. Use the derivatives to explain why the families of curves form orthogonal
trajectories. y = mx; x² + y² = a²
, where m and a are constants

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