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Differential Equations
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Orthogonal Trajectories of a given family of curves
Let
f(x,y,c) = 0
is the family of curves.
Differentiating and eliminating c, we get
F(x,y,y') = 0
, where y' is the slope of the curve.
The differential equation of the family of orthogonal curve is given by
F(x,y,-1/y') = 0
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