Explanation

(b)
$\frac{dy}{dx} = - \left( \frac{\cos{x - \sin x}}{\sin{x + \cos x}} \right)$
$\Rightarrow dy = - \left( \frac{\cos{x - \sin x}}{\sin{x + \cos x}} \right)dx$
On integrating both sides, we get
$y = - \log{(\sin{x + \cos{x) + \log c}}}$
$\Rightarrow y = \log\left( \ \frac{c}{\sin{x + \cos x}}\ \right)$
$\Rightarrow e^{y} = \frac{c}{\sin{x + \cos x}}$
$\Rightarrow e^{y}\left( \sin{x + \cos x} \right) = c\$