A particle of mass $m$ and electric charge $q$ moves under the 
influence of a constant magnetic field of the form
${\bf B}({\bf r})\!=\!B_0\hat{\bf z}$. Obtain the most general 
solution for the velocity ${\bf v}(t)$ using Newton's second
law of motion in combination with the Lorentz force. That is,
$$ {\bf F}=m{\dot{\bf v}}=\frac{q}{c}{\bf v}\times{\bf B}\;.  $$
