how do you separate these variables dy/dx=1/y^2, y(0)=4

Answer 1

y^2 dy = dx
(1/3) y^3 = x + c
but (0,4) is on it so
(1/3)(4^3) = c
c = 64/3
so
y^3/3 = x + 64/3
y^3 = 3 x + 64