Q. The differential equation $\cot{\ y\ dx = x\ dy}$ has a solution of the form
A) $y = \cos x$
B) $x = c\sec y$
C) $x = \sin y$
D) $y = \sin x$
Explanation
(b)
Given, $\cot{\ y\ dx = x\ dy}$
$\Rightarrow \frac{dx}{x} = \frac{dy}{\cot y}\ \Rightarrow \frac{dx}{x} = \tan{y\ dy}$
On integrating both sides, we get
$\int_{}^{}{\frac{1}{x}dx = \int_{}^{}{\tan{\bullet y\ dy}}}$
$\Rightarrow \log{x = \log{\sec{y + \log c}}}$
$\Rightarrow \log{x = \log{c\sec y}}$
$\Rightarrow x = c\sec y$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.