The solution of dydx=1−x2−y2+x2y2−−−−−−−−−−−−−−−√ is | Filo
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The solution of dydx=1−x2−y2+x2y2−−−−−−−−−−−−−−−√ is

  1. sin−1y=sin−1x+c
  2. 2sin−1y=1−x2−−−−−√+sin−1x+c
  3. 2sin−1y=x1−x2−−−−−√+sin−1x+c
  4. 2sin−1y=x1−x2−−−−−√+cos−1x+c
Correct Answer: Option(d)
Solution: [c] ∵dydx=1−x2−y2+x2y2−−−−−−−−−−−−−−−√ dydx=(1−x2)(1−y2);−−−−−−−−−−−−−√⇒dy1−y2−−−−−√=1−x2−−−−−√.dx ⇒∫dy1−y2−−−−−√=∫1−x2−−−−−√.dx [integrating b/s] ⇒sin−1(y1)=x21−x2−−−−−√+12sin−1(x1)+c ⇒2sin−1y=x1−x2−−−−−√+sin−1x+c where c is an arbitrary constant.
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