I am trying to solve the differential equation that will give me the equation of motion of a point charge under the influence of another point charge's electric field. Say point charge A is free to move, and it currently a distance D away from point charge B. Point charge B is fixed in space. Say charge A has q = +q, and charge B has q = -q. The two charges will attract. Ignoring all other influences (gravity, etc), charge A should experience a force F = qE, where E is the field due to charge B, or: F = -(k q^2)/r^2 where k = 1/4πε (imagine that ε is the permittivity of free space; I'm using the available symbols) Solving for equations of motion, I use: ma = -(k q^2)/r^2 or a = -(k q^2)/(m r^2) Putting it another way, r → r[t], a → r''[t] Then I get: r[t]2 r''[t] = -(k q^2)/m Or r[t]2 r''[t] = C How do I solve that differential equation? It is a 2nd order non-linear diff eq... The Mathematica answer I get is very complicated, but I'm hoping someone can help me out with this one. Also, I can use the following initial conditions: r=D r'=0 Thanks!