In this paper, a new space-time nonlinear transformation is proposed and applied to a class of time-varying nonlinear systems. Then the integrability condition of the system is derived by coordinate transformation, and the linear differential equation with constant coefficients is obtained. Based on the inverse nonlinear transformation and the analytic solution of linear differential equations with constant coefficients, the exact solution of the original system is derived. The 1/2 order Bessel equation is taken as a special case of this kind of time-varying nonlinear system, and its exact solution is obtained by using this theory. Finally, the effectiveness and correctness of the proposed method are verified by some numerical simulations.