differentiation...?

Question

how to solve
x^3 - 8x^2y^2 + y = 9x?

Answer 1

x^3 - 8x^2y^2 + y = 9x

3x^2 - (16x)(y^2) + (2y)(y')(8x^2) + y' = 9

9 - 3x^2 + (16x)(y^2) - y' = (2y)(y')(8x^2)

y' = [9-3x^2+(16x)(y^2)-y'] / (16x^2y)

y' + y'/(16x^2y) = y'(1+1/(16x^2y))

y' = [9-3x^2+(16x)(y^2)] / [(16x^2y)(1+1/16x^2y)]

You can simplify this one more step using algebra.

hint: it's in the denominator

Answer 2

x^3 - 8x^2y^2 + y = 9x
x^3 - 8x^2*y^2 + y - 9x = 0
now use ln differntiation

Answer 3

This equation has two unknown.To solve give a value to x and find y (Ex. x=-1 so-1-8y^2+y=-9 and solve for y)
If yo want to find out y´

3x^2 -16x*y^2+16x^2 y*y´+y´=9 so y´= (9-3x^2+16xy^2)/(1+16x^2y)