حل dy/cosy=-dx/sinx

$$\frac { d y } { \cos y } = - \frac { d x } { \sin x }$$

برای d حل کنید

$$\left\{\begin{matrix}d=0\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }y=\pi n_{1}+\frac{\pi }{2}\text{ and }\nexists n_{2}\in \mathrm{Z}\text{ : }x=\pi n_{2}\\d\in \mathrm{R}\text{, }&\frac{x}{\sin(x)}+\frac{y}{\cos(y)}=0\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }y=\frac{\pi \left(2n_{1}+1\right)}{2}\text{ and }\nexists n_{2}\in \mathrm{Z}\text{ : }x=\pi n_{2}\end{matrix}\right.$$