Let ;

**phai(x,y,dy/dx)=0**be a given differential equation and

let ;

**f(x,y,c)=0**be its general solution .

Now it is known that the envelope of any family of curves

**f(x,y,c)=0****---------- (1)**

is contained in the locus obtained on eliminating ,

*between*

**c****(1)**and

**[delta f(x,y,c)]/[delta c]=0****--- (2)**

Let this eliminate be ,

**sai (x,y)=0****---------- (3)**

As the elimination given by

**(3)**may represent loci other than the envelope .

It is necessary to verify if any part of locus represented by

**(3)**is or is not a solution of the given differential equation .

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