EDB — 240

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Remark 18

[240]The envelope curve has an important property in the field of differential equations. Suppose \(y=f_ a(x)\) 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 \(g=f_ a\) \(g'=f_ a'\) at a point \(x\) then they coincide in a neighborhood.
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