Q. The solution of differential equation $\left( \sin x + \cos x \right)dy + \left( \cos x - \sin x \right)dx = 0$ is
A) $e^{x}\left( \sin x + \cos x \right) + c = 0$
B) $e^{y}\left( \sin x + \cos x \right) = c$
C) $e^{y}\left( \cos x - \sin x \right) = c$
D) $e^{x}\left( \sin x - \cos x \right) = c$
Explanation
(b)
Given, $dy = - \left( \frac{\cos x - \sin x}{\sin x + \cos x} \right)dx$
$\Rightarrow$ $y = - \log{(\sin x + \cos x)} + \log c\ \ \$ [integrating]
$\Rightarrow$ $y = \log\left( \frac{c}{\sin x + \cos x} \right)$
$\Rightarrow$ $e^{y}\left( \sin x + \cos x \right) = c\$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.