# Solution of ODE

1. May 18, 2010

### Acut

How can this equation be solved?

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

2. May 18, 2010

### Cyosis

By separation of variables.

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

Now you can integrate both sides.

3. May 19, 2010

### Unit

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

4. May 19, 2010

### Acut

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

5. May 22, 2010

### 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.