Which one of the following is the solution of the differential equation $x^2 \frac{d y}{d x}+9 x y=x^4(\text { for } x\gt0)$ given that $y=0$ when $x=1$ ?

• Correct answer
  A

  $12 y=x^3-\frac{1}{x^9}$
• B

  $12 y=x^9-\frac{1}{x^3}$
• C

  $9 y=x^{21}-\frac{1}{x^3}$
• D

  $9 y=x^3-\frac{1}{x^{21}}$

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