relativistic rocket equation

[CPL.Luke]

So I was playing around with the idea of a relativistic rocket equation, and in the process of deriving it I ran into a differential equation that I can't seem to solve.

 

v_e dm= m(1+mu^2 (gamma)^2) du

 

its first order but I can't seem to figure out how to solve it, m is the rest mass (which changes because its a rocket) u is the velocity of the rocket, and gamma is the relativistic factor

 

gamma= (1-v^2/c^2)^(-1/2)

 

any help solving it would be greatly appreciated, I tried seeing if I could use integration by parts on it and then subsequently differentiating, but that method seemed dubious at best.

[Janus]

Why not just use the ones already in existance:

http://en.wikipedia.org/wiki/Relativistic_rocket

 

Unless it just a exercise in deriving them yourself. In which case, isn't asking for help cheating?

[CPL.Luke]

it is an exercise in deriving it, but it appears that some trick is needed to solve the de, and I'd much rather here about the trick here and maybe discuss the physics with somebody than read a wikipedia article.

[timo]

Perhaps you should show the "process of deriving it" here. The term [math] 1 + m\, u^2 \, \gamma^2 [/math] looks quite suspicious by itself: You are adding a dimensionless number and an energy-like term there.