general solution of differential equation

$\displaystyle \frac{dy}{dx} = x(1-x) $

$\displaystyle dy = x(1-x) dx $

$\displaystyle dy = x-x^{2} dx $

$\displaystyle \int dy = \int x-x^{2} dx $

is this so far correct? cuse my book gives me a solution like this $\displaystyle \int \frac{1}{x(1-x)} = \int dy $

And i have no idea how they got this?

Re: general solution of differential equation

what you have written is correct. But are you sure you have copied the problem correctly? If the problem were

$\displaystyle \frac{dy}{dx}= y- y^2$ then you would have $\displaystyle \int\frac{dy}{y- y^2}= \int dx$.