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

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.

• Its Bernouilli's equation – Aryadeva Apr 14 '20 at 1:45
• Please don't change the original equation. – Aryadeva Apr 14 '20 at 1:51

## 1 Answer

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