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NDA 2011
Exam
NDA
Year
2011
Subject
Mathematics
Chapter
Differential Equations

NDA 2011 · Mathematics · Differential Equations

What is the solution of the differential equation (d y)/(d x)+...

What is the solution of the differential equation dydx+1−y21−x2=0?\frac{d y}{d x}+\sqrt{\frac{1-y^2}{1-x^2}}=0 ? where cc is a constant.

Options

  1. Asin⁡−1y+sin⁡−1x=c\sin ^{-1} y+\sin ^{-1} x=c
  2. Bsin⁡−1y−sin⁡−1x=c\sin ^{-1} y-\sin ^{-1} x=c
  3. C2sin⁡−1y+sin⁡−1x=c2 \sin ^{-1} y+\sin ^{-1} x=c
  4. D2sin⁡−1y−sin⁡−1x=c2 \sin ^{-1} y-\sin ^{-1} x=c

Correct answer

A. sin⁡−1y+sin⁡−1x=c\sin ^{-1} y+\sin ^{-1} x=c

Step-by-step solution

dy1+y2+dx1−x2=0\frac{d y}{\sqrt{1+y^2}}+\frac{d x}{\sqrt{1-x_2}}=0 on integration sin⁡−1y+sin⁡−1x=C\sin ^{-1} y+\sin ^{-1} x=C
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