JEE Math Practice Question

Let $$y = y(x)$$ be the solution curve of the differential equation $${{dy} \over {dx}} = {y \over x}\left( {1 + x{y^2}(1 + {{\log }_e}x)} \right),x > 0,y(1) = 3$$. Then $${{{y^2}(x)} \over 9}$$ is equal to :

1. A.$${{{x^2}} \over {5 - 2{x^3}(2 + {{\log }_e}{x^3})}}$$
2. B.$${{{x^2}} \over {3{x^3}(1 + {{\log }_e}{x^2}) - 2}}$$
3. C.$${{{x^2}} \over {7 - 3{x^3}(2 + {{\log }_e}{x^2})}}$$
4. D.$${{{x^2}} \over {2{x^3}(2 + {{\log }_e}{x^3}) - 3}}$$