Initial value problem $y' = y(2-y)$

Question

I wish to solve the differential equation,

$$\frac{dy}{dx} = y(2-y)$$ with initial condition $y(0) = 1$. I'm new to differential equations, and I've never seen an equation with only one variable like this. From what I understand, it's an ordinary differential equation but I don't know what that means or what methods I should use to solve it.

Answer 1

Hint: it is a separable DE and use $$ \frac{1}{y(2-y)}=\frac12\left(\frac{1}{y}+\frac{1}{2-y}\right). $$