1. The problem statement, all variables and given/known data I am asked to find r(t) for a charged q particle in an magnetic undulator. Wrote down these equations: x'' = w* y' *cos(a*x) (1) y'' = -w* x' *cos(a*x) (2) z'' = 0 (3) r(0) = (x0, y0, z0); r(0)' = (x0', y0', z0'). 2. Relevant equations Not sure how to go on solving these. 3. The attempt at a solution z(t) is obvious. I am able to integrate (2) once to find y' = -w/a *sin(a*x) + C. Plugging it into (1) doesn't seem to do any progress, since I get x'' = - w^2 /a *sin(a*x)*cos(a*x) + C*w*cos(a*x). Because particle is in magnetic field, it's known that sqrt(x'^2 + y'^2 + z'^2) = constant from r(0)', but not sure how to use it to my advantage.