GATE Civil Engineering

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Consider the following differential equation:

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

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

- $\frac{x}{y} \cos \frac{y}{x} = c$
- $\frac{x}{y} \sin \frac{y}{x} = c$
- $xy \cos \frac{y}{x} = c$
- $xy \sin \frac{y}{x} = c$

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