MCQ
The differential equation $\cot y\,\,dx = x\,\,dy$ has a solution of the form
- A$y = \cos x$
- ✓$x = c\sec y$
- C$x = \sin y$
- D$y = \sin x$
✓
Answer
Correct option: B.
$x = c\sec y$
b
(b) $\cot y.dx = x.dy$ ==> $\frac{{dx}}{x} = \frac{{dy}}{{\cot y}}$ ==> $\frac{{dx}}{x} = \tan y.dy$
(b) $\cot y.dx = x.dy$ ==> $\frac{{dx}}{x} = \frac{{dy}}{{\cot y}}$ ==> $\frac{{dx}}{x} = \tan y.dy$
Integrating both sides,
$\log x = \log \sec y + \log c$ ==> $x = c\sec y$.
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