I have been attempting to construct vector valued functions that model the motion of a simple pendulum. Thus far, I obtained an equation to model acceleration and was attempting to find an equation to model the velocity. However, the differential equation that must be solved seems very difficult, if not impossible, to solve. Solving the x component of velocity requires solving this differential equation:
Is it possible to find a solution? I have tried a variety of substitutions and done research to attempt to determine an integration factor, but to no avail.