Question

Suppose you want to find an equation for a curve whose slope at any point (x, y) is x/(6y^2).

You'd need to solve the differential equation dy/dx = x/(6y^2).


Using separation of variables to solve this equation, you get (where C is an arbitrary constant of integration)

Answer 1

6y^3= x^2 + C
3y^3 = 2x^2 + C
1/3y^3 = 1/2x^2 + C
2y^3 = x^2 + C
2y^3 = 1/2x^2 + C

Answer 2

What do you think?

Answer 3

The last one @Loser66

Answer 4

yup