求解 dy/dx=cosxcos^2y/sinx

$$\frac { d y } { d x } = \frac { \cos x \cos ^ { 2 } y } { \sin x }$$

求解 x 的值

$$\left\{\begin{matrix}\\x=\pi n_{1}+\frac{\pi }{2}\text{, }n_{1}\in \mathrm{Z}\text{, }&\text{unconditionally}\\x\neq \pi n_{2}\text{, }\forall n_{2}\in \mathrm{Z}\text{, }&\exists n_{1}\in \mathrm{Z}\text{ : }y=\pi n_{1}+\frac{\pi }{2}\end{matrix}\right.$$

求解 y 的值

$$\left\{\begin{matrix}y=\pi n_{2}+\frac{\pi }{2}\text{, }n_{2}\in \mathrm{Z}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}\\y\in \mathrm{R}\text{, }&\exists n_{2}\in \mathrm{Z}\text{ : }x=\pi n_{2}+\frac{\pi }{2}\end{matrix}\right.$$