Application of the elliptic balance method to a nonlinear singular oscillator

New analytical approximate solutions based on Jacobi elliptic functions are formulated to compute the angular frequency value of a nonlinear singular oscillator. It is shown that when our derived analytical angular frequency solutions are compared to the exact angular frequency value, the third-order elliptic balance solution provides the best estimate to the exact value since the percentage error value is about 0.0059% which is 216 times lower than the best estimate percentage error value reported in the literature.