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

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

Grade:12

2 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 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
askIITians Faculty 86 Points
one year ago
hello student

642-2208_differential equation 2 .png


Hope it helps
Thankyou

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