Field Method for Integrating the First Order Differential Equation
2007
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.
Keywords:
- First-order partial differential equation
- Mathematical optimization
- Universal differential equation
- Method of characteristics
- Separable partial differential equation
- Integrating factor
- Bernoulli differential equation
- Homogeneous differential equation
- Mathematics
- Differential equation
- Mathematical analysis
- Hyperbolic partial differential equation
- Ordinary differential equation
- Exact differential equation
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