The general solution of the differential equation $\left(x \sin \frac{y}{x}\right) d y=\left(y \sin \frac{y}{x}-x\right) d x$ is

• Correct answer
  A

  $\cos \left(\frac{y}{x}\right)=\log |x|+c$
• B

  $\cos \left(\frac{y}{x}\right)=\frac{1}{x}+c$
• C

  $\cos \left(\frac{x}{y}\right)=\log |y|+c$
• D

  $\cos \frac{\mathrm{y}}{\mathrm{x}}=\frac{2}{\mathrm{x}}+\mathrm{c}$

Hence, the correct answer is option: 'A'.