Thread: general solution of differential equation

1. general solution of differential equation

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

$dy = x(1-x) dx$

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

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

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

And i have no idea how they got this?

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