Solving ODE: $\frac{dx}{dt}=ax(b-x)$

[Acut]

How can this equation be solved?

$$\frac{dx}{dt}$$=ax(b-x)

 

[Cyosis]

By separation of variables.

$$\frac{dx}{ax(b-x)}=dt$$

Now you can integrate both sides.

 

[Unit]

The integral of the dx side requires decomposition into partial fractions.

 

[Acut]

Many thanks!
I'm a bit rusty in solving ODE's and was having a hard time trying to solve this one..

 

[IPhO' 2008]

dx/(ax(b-x)) = dx/abx + dx/ab(b-x)
= dx/abx - d(b-x)/ab(b-x)
and then you can integrate these terms.