The general solution of the differential equation $(x-y)^2 \frac{d y}{d x}=a^2$ is

• A

  $y=a \log \left(\frac{x-y+1}{x+y-1}\right)+c$
• Correct answer
  B

  $y=\frac{a}{2} \log \left(\frac{x-y-a}{x-y+a}\right)+c$
• C

  $y=\frac{a}{2} \log \left(\frac{x+y-a}{x-y-a}\right)+c$
• D

  $y=\frac{a}{4} \log \left(\frac{x-y+a}{x+y+a}\right)+c$

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