In this paper, a new technique to obtain a fundamental solution is developed. The well-known Cayley-Hamilton theorem in linear algebra is adopted to obtain the inverse of the differential operator (in its symbolic form) of the governing equation and hence the corresponding fundamental and particular solutions are obtained. Several examples are presented to demonstrate the use of the presented technique.

中文翻译：

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基本解和凯利-汉密尔顿公式


在本文中，开发了一种获得根本解决方案的新技术。采用线性代数中著名的凯莱-汉密尔顿定理求得控制方程微分算子（符号形式）的逆，从而得到相应的基本解和特解。提供了几个示例来演示所提出的技术的使用。