# Solution of ODE

#### Acut

How can this equation be solved?

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

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#### Cyosis

Homework Helper
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.