Solved: PROBLEM 14RP

Chapter , Problem 14RP

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When all the curves in a family \(G\left(x, y, c_{1}\right)=0\) intersect orthogonally all the curves in another family \(H\left(x, y, c_{2}\right)=0\), the families are said to be orthogonal trajectories of each other. See Figure 3.R.4. 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  1f(x, y). In Problems 13 and 14 find the differential equation of the given family. Find the orthogonal trajectories of this family. Use a graphing utility to graph both families on the same set of coordinate axes.

\(y=\frac{1}{x+c_{1}}\)

Text Transcription:

G(x, y, c_1) = 0

H(x, y, c_2) = 0

y=\frac{1}{x+c_{1}}

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