CBSE Class 12-science Answered

Dear Student

y=[(1-x)/(1+x)]^1/2

y²=(1-x)/(1+x).................................(1)

2ydy/dx = -2/(1+x)²

Cancelling '2' from both sides, and multiplying 'y' on both sides, we get

y²dy/dx = -y/(1+x)²

Substituting the value of y² from eqn (1)

(1-x)/(1+x) dy/dx = -y/(1+x)²

(1-x)(1+x)dy/dx = -y

(1-x²)dy/dx + y =0

Hence the question is wrong. It should be '(1-x²)' in place of (1-x).

Let us cross check by integrating the expression to be proved:

(1-x)dy/dx+y=0

-dy/y=dx/(1-x)

-lny=-ln(1-x)+C ……………………..(where C is any constant)

y=(1-x)+C’ ………………………….(where C’ is any constant)

This expression DOES NOT match with the one given in the question! Hence the question is wrong.

 Regards Topperlearning.