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Differential Calculus> if y= sqrt(1-x/1+x) prove that (1 – x^2)d...

question mark

if y= sqrt(1-x/1+x) prove
that (1 – x^2)dy/dx + y = 0

taniska , 10 Years ago

Grade 12

2 Answers

Jitender Singh

Last Activity: 10 Years ago

Ans:
Hello Student,
Please find answer to your question

$y = \sqrt{\frac{1-x}{1+x}}$
$y = \sqrt{\frac{(1-x).(1-x)}{(1+x).(1-x)}}$
$y = \frac{(1-x)}{\sqrt{1-x^{2}}}$ ….....(1)
$\frac{dy}{dx} = \frac{\sqrt{1-x^{2}}.(-1)-(1-x).\frac{-x}{\sqrt{1-x^{2}}}}{(\sqrt{1-x^{2}})^{2}}$
$\frac{dy}{dx} = \frac{-\sqrt{1-x^{2}}.+(1-x).\frac{x}{\sqrt{1-x^{2}}}}{({1-x^{2}})}$
$(1-x^{2})\frac{dy}{dx} = {-\sqrt{1-x^{2}}.+(1-x).\frac{x}{\sqrt{1-x^{2}}}}$
$(1-x^{2})\frac{dy}{dx} = \frac{-1+x^{2}+x-x^{2}}{\sqrt{1-x^{2}}}$
$(1-x^{2})\frac{dy}{dx} = \frac{-1+x}{\sqrt{1-x^{2}}}$
$(1-x^{2})\frac{dy}{dx} = -(\frac{1-x}{\sqrt{1-x^{2}}})$
From (1)
$(1-x^{2})\frac{dy}{dx} = -y$
$(1-x^{2})\frac{dy}{dx} + y = 0$

Ajeet Tiwari

Last Activity: 4 Years ago

hello student

642-2208_differential equation 2 .png

Hope it helps
Thankyou

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