Field Method for Integrating the First Order Differential Equation

An important modern method in analytical mechanics for finding the integral,which is called the field-method,is used to research the solution of a differential equation of the first order.First,by introducing an intermediate variable,a more complicated differential equation of the first order can be expressed by two simple differential equations of the first order,then the field-method in analytical mechanics is introduced for solving the two differential equations of the first order.The conclusion shows that the field-method in analytical mechanics can be fully used to find the solutions of a differential equation of the first order,thus a new method for finding the solutions of the first order is provided.