Consider the following differential equation:

$$x(y\:dx +x\:dy) \cos \dfrac{y}{x}=y(x\:dy-y\:dx) \sin \dfrac{y}{x}$$

Which of the following is the solution of the above equation ($c$ is an arbitrary constant)?

1. $\dfrac{x}{y} \cos \dfrac{y}{x} = c \\$
2. $\dfrac{x}{y} \sin \dfrac{y}{x} = c \\$
3. $xy \cos \dfrac{y}{x} = c \\$
4. $xy \sin \dfrac{y}{x} = c$