dy/dx=(6x^2 *y^2)

Answer 1

dy/dx=(6x^2 *y^2)
dy/y^2 = 6x^2 dx
-1/y = 2x^3 + c
y = -1/(2x^3+c)
or
y = 1/(c-2x^3) (different c)

Answer 2

why 1/y? that the only thing I don't get.

Answer 3

huh? did you forget the power rule?
∫ 1/y^2 dy = -1/y