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Concept explainers
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). In Problems 15-18 find 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.
16. x2 − 2y2 = c1
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Chapter 3 Solutions
Student Solutions Manual For Zill's A First Course In Differential Equations With Modeling Applications, 11th
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,
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