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**housefire** Okay, I have a question about motion with ODEs and I've gone round so many times and tried it in so many ways that I don't have a clue if I'm on the right line at all any more. I've ended up with this equation, where z is a function of time, t, with the rest of the unknowns as various constants. I'm trying to solve it for z but I'm having a mental block now so I'm asking for help.

Okay, I have a question about motion with ODEs and I've gone round so many times and tried it in so many ways that I don't have a clue if I'm on the right line at all any more. I've ended up with this equation, where z is a function of time, t, with the rest of the unknowns as various constants. I'm trying to solve it for z but I'm having a mental block now so I'm asking for help.

$\displaystyle \ln|z|+\frac{z}{a} = \frac{b}{g}+1$

Of course, there's a good chance I've screwed up the math before getting to this so it might not even work, in which case I may have to go and bang my head against a wall a few times..