Exact solution of a quadratic nonlinear oscillator

The exact solution of a quadratic nonlinear oscillator (QNO) is presented by using the Jacobian elliptic sine function. The constants in the solution are expressed in terms of the initial conditions. The formulas for the period of oscillation T and amplitude B (for x ⩽ 0 ) are also given. This exact solution can serve as a benchmark solution for various approximate solutions. It also can be utilized for educational purpose.