The major aim of this article is to find the analytical solution of the physics-based model for lithium-ion batteries. Because the full-order pseudo two-dimensional model, comprised of a nonlinear algebraic-differential system, has a high computational cost, single particle model (SPM) is considered in this work to lessen the computational burden. First, the governing partial differential equations of the SPM are simplified with the volume average method along with polynomial approximations, and then an exact analytical solution of the simplified differential system is computed with the integrating factor method. The accuracy and reliability of the proposed analytical solution are accessed by comparing discharge curves simulation data with PyBAMM simulations in different operating conditions. It is observed that the error varies between 10 mV–25 mV for low to higher C-rate and the maximum error occurs at the middle and terminal points of the discharge cycling step in most cases. Finally, discharge curves are simulated with the help of the proposed analytical solution for the NMC battery, and then simulation results are compared with the experimental data of the NMC 50 Ah commercial battery. It is observed that the error in simulations is about 1% relative to terminal voltage.