کاربرد تبديل لاپلاس در حل معادلات دیفرانسیلی

Abstract

One of the methods used to solve differential equations with initial conditions is the Laplace transform method. This method can also solve certain differential equations involving non-continuous functions. Before discussing the method, we introduce the Laplace transform, the property of linearity, and the necessary and sufficient conditions for existence. We also cover the inverse Laplace transform, the inverse Laplace transform as a linear operator, and the process of solving differential equations. Additionally, some integrals are computed using the Laplace method, which converts the differential equation into an algebraic equation. After solving it and obtaining the inverse Laplace transform, the equation is solved. Integral transforms are also referred to as Laplace transforms.