拉普拉斯变换在求微分方程初解时的应用

The Application of Laplace Transform in Solving the Deferential Equation

拉普拉斯变换是高等数学中最常见的一种运算方法,运用拉普拉斯变换解常微分方程,可将复杂的运算过程简单化.因此,通过掌握拉普拉斯变换的定义及主要性质,并依据问题进行分析,概括出拉普拉斯变换在求解微分方程初解时的基本步骤,以此来强化对这一方法的理解.

Some knowledge is relatively complicated in the higher mathematics. Methods of Transfor—mations are often used in order to make calculation process more concise. Laplace transform is one of the most common methods of them. Gomplex calculation process can be simplified in solving the ODE （ordi—nary differential equations） by Laplace transform. Therefore, the thesis summarized the basic steps in solving differential equations used the Laplace transform by mastering the definition and main properties of Laplace transform, and analyzing according to different problems, and thus strengthened a profound un—derstanding of this method.