Answered: amilies on the same set of coordinate…

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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When all the curves in a family G(x, y, c1) = 0 intersect orthogonally all the curves in another family H(x, y, c2) =0, the families are said to be orthogonal trajectories of each other. See
Figure 3.R.5. If dy/dx = f(x, y) is the differential equation of one family, then the differential equation for the orthogonal trajectories of this family is dy/dx =-1/f(x, y).
the differential equation of the given family by computing dy/dx
and eliminating c1 from this equation. Then Find the orthogonal trajectories of the family. Use a graphing utility to graph both
families on the same set of coordinate axes.

1- y = c1x

2- y =c1e^x

QUATIONS
G(x, y, c1) = 0
tangents
H(x, y, c2) =0
FIGURE 3.R.5 Orthogonal families

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