Verified answer

x^3(x+y) = y^2(9x-y) --->Product Rule

3x^2(x+y) + x^3(1+y') = 2yy'(9x-y) + y^2(9-y') --->Expand some parenthesis

3x^2(x+y) + x^3 + x^3y' = 2yy'(9x-y) + 9y^2 - y'y2 --->Separate y-primes (y')

4x^3 + 3x^2y - 9y^2 = -x^3y' + 2yy'(9x-y) - y'y^2 ---> Fix right-hand side

4x^3 + 3x^2y - 9y^2 = y'(-x^3 + 2y(9x-y) - y^2) ---> Fix right-hand side

4x^3 + 3x^2y - 9y^2 = y'(-x^3 + 18yx - 3y^2) ---> Fix right-hand side

4x^3 + 3x^2y - 9y^2

----------------------------- = y'

(-x^3 + 18yx - 3y^2)

(Note that I'm ignoring the d/dy which is very important to NOT ignore)