Let 4xy^3 - x^2y= 5x - 6 - x^3 where y is a differential of X. Find y' in terms of x and y.

Question

I get: y'= -4y^3 - 2xy + 3x^2 -5 / x^2 -12xy^2
My answer handout shows the answer as positive. Which should it be, neg. or pos.? Thanks

Answer 1

4xy^3 - x^2y = 5x - 6 - x^3

4y^3 + 12xy^2y' - 2xy - x^2y' = 5 - 3x^2
y'(12xy^2 - x^2) = 5 - 3x^2 - 4y^3 + 2xy
y' = - (3x^2 - 2xy + 4y^3 - 5)/(12xy^2 - x^2)

or

(3x^2 - 2xy + 4y^3 - 5)/(x^2 - 12xy^2)

Not quite what you had