Saturday, 22 February 2014

Determination of Singular Solutions

 



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 ,    c      between  (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 .




No comments:

Post a Comment

Our Latest Post

How to find log (alpha+ i beta), Where alpha and beta are real

Here is the video to show the details of solving this problem. It is an important problem for basic understanding about the logarithm of re...

Popular Post