The pseudo-linearization and any order approximate analytical solutions for nonlinear dynamical equation

The integrand is expanded as the Taylor series, at the initial state of time-state space, by introducing the concept of time-state space and the method of pseudo-linearization. The any order approximate general analytical solutions are obtained by directed integrating, and proven to be convergent. Compared with the general method of linear or nonlinear removal, this method can simplify the calculation for non-commutative system and commutative time-varying system. The method is also proven to be universal.