If y = (1 - x)(1 + x) , then - Vidyadip

MCQ

If $y = \sqrt {(1 - x)(1 + x)} $, then

A
$(1 - {x^2}){{dy} \over {dx}} - xy = 0$
✓
$(1 - {x^2}){{dy} \over {dx}} + xy = 0$
C
$(1 - {x^2}){{dy} \over {dx}} - 2xy = 0$
D
$(1 - {x^2}){{dy} \over {dx}} + 2xy = 0$

✓

Answer

Correct option: B.

$(1 - {x^2}){{dy} \over {dx}} + xy = 0$

b
(b) ${y^2} = (1 - {x^2})$ ==>$2y\frac{{dy}}{{dx}} = - 2x$ or

$\frac{{dy}}{{dx}} = \frac{{ - x}}{y} = \frac{{ - xy}}{{(1 - {x^2})}}$ or

$(1 - {x^2})\frac{{dy}}{{dx}} + xy = 0$.

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