求解 dy/dx=tany/siny-x

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

求解 x 的值

$$x\neq \sin(y)$$

$$\exists n_{1}\in \mathrm{Z}\text{ : }y=\pi n_{1}$$

求解 y 的值

$$y=\pi n_{3}$$

$$n_{3}\in \mathrm{Z}$$

$$\left(\exists n_{1}\in \mathrm{Z}\text{ : }\left(n_{1}>\frac{n_{3}}{2}-\frac{5}{4}\text{ and }n_{1}<\frac{n_{3}}{2}-\frac{3}{4}\right)\text{ or }\left(x<0\text{ and }x\geq -1\text{ and }\exists n_{1}\in \mathrm{Z}\text{ : }\left(n_{1}\geq \frac{n_{3}}{2}-\frac{7}{4}\text{ and }n_{1}<\frac{n_{3}}{2}-\frac{3}{4}\right)\right)\text{ or }\left(x>0\text{ and }x\leq 1\text{ and }\exists n_{1}\in \mathrm{Z}\text{ : }\left(n_{1}>\frac{n_{3}}{2}-\frac{5}{4}\text{ and }n_{1}\leq \frac{n_{3}}{2}-\frac{1}{4}\right)\right)\right)\text{ and }\left(\left(x\geq -1\text{ and }x<0\text{ and }\exists n_{2}\in \mathrm{Z}\text{ : }\left(n_{2}>\frac{n_{3}}{2}-\frac{3}{4}\text{ and }n_{2}\leq \frac{n_{3}}{2}+\frac{1}{4}\right)\right)\text{ or }\left(x>0\text{ and }x\leq 1\text{ and }\exists n_{2}\in \mathrm{Z}\text{ : }\left(n_{2}\geq \frac{n_{3}}{2}-\frac{5}{4}\text{ and }n_{2}<\frac{n_{3}}{2}-\frac{1}{4}\right)\right)\text{ or }\left(\exists n_{2}\in \mathrm{Z}\text{ : }\left(n_{2}>\frac{n_{3}}{2}-\frac{3}{4}\text{ and }n_{2}<\frac{n_{3}}{2}-\frac{1}{4}\right)\text{ and }|x|\leq 1\right)\right)$$

$$x\geq -1\text{ and }x\leq 1$$