Hello!

I have been given an equation as following;

$\displaystyle \frac{dy}{dt}=ay(A-y)$

where

$\displaystyle y>0$

$\displaystyle A$ and $\displaystyle a$ are positive constants

1)

I am then to find the constants $\displaystyle \alpha$ and $\displaystyle \beta$ so the equation can be given as this:

$\displaystyle \frac{1}{y(A-y)}= \frac{\alpha}{y}+ \frac{\beta}{A-y)}$

2)

And at last find a general solution when $\displaystyle y(0)= \frac{A}{2}$

Don't know where to start actually...

Any help is greatly appreciated!