Differential equation for a rocket

[DontDeimos]

Homework Statement

A rocket through interstellar dust, no gravity. Solve for v with respect to mass.

k is a constant.
Drag = -bv

Homework Equations

[/B]

The Attempt at a Solution

To start:

It should become a separable differential equation, but I am having a lot of trouble solving it for v(m). A hint that was given, is in the final equation you should have has m/m0 to a power.

 

[dcnairb]

You could divide by $-u - \frac{b}{k} v$ and also by $m$ and then multiply by $dm$ to get

$$\frac{dv}{-u - \frac{b}{k} v} = \frac{dm}{m}$$

This is solvable, see if it gets you the answer you need--I feel like both terms' logarithmic solutions would cancel but because of the coefficients perhaps you will get the correct dependence when you solve for it.