EDB — 240

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Remark 18

[240]The envelope curve has an important property in the field of differential equations. Suppose y=fa(x) are solutions of the differential equation Φ(y,y,x)=0: then also g is solution (immediate verification). 1

  1. With equations in normal form, however, this notion is not interesting because there is local uniqueness and then there can be no special solutions; that is, if g=fa g=fa at a point x then they coincide in a neighborhood.
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