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)?
- $\dfrac{x}{y} \cos \dfrac{y}{x} = c \\$
- $\dfrac{x}{y} \sin \dfrac{y}{x} = c \\$
- $xy \cos \dfrac{y}{x} = c \\$
- $xy \sin \dfrac{y}{x} = c$