If $x \log x \frac{d y}{d x}+y=\log x^2$ and $y(e)=0$, then $y\left(e^2\right)=$

• A

  $0$
• B

  $1$
• C

  $\frac{1}{2}$
• Correct answer
  D

  $\frac{3}{2}$

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