Solve y^prime=-3y-e^x/3x+cosy

$$y ^ { \prime } = \frac { - 3 y - e ^ { x } } { 3 x + \cos y }$$

Solve for x

$$x=\ln(-3y)$$

$$\ln(-3y)\neq -\frac{\cos(y)}{3}\text{ and }y<0$$

Solve for y

$$y=-\frac{e^{x}}{3}$$

$$\exists n_{2}\in \mathrm{Z}\text{ : }\left(n_{2}>-\frac{e^{x}+3\arccos(3x)+3\pi }{6\pi }\text{ and }n_{2}<\frac{-e^{x}-3\arccos(3x)+3\pi }{6\pi }\right)\text{ and }|x|\leq \frac{1}{3}\text{ and }\exists n_{1}\in \mathrm{Z}\text{ : }\left(n_{1}>\frac{\frac{-e^{x}+3\arccos(3x)}{\pi }-9}{6}\text{ and }n_{1}<\frac{-e^{x}+3\arccos(3x)-3\pi }{6\pi }\right)\text{ and }x\neq -\frac{\cos(\frac{e^{x}}{3})}{3}$$