Solve the differential equation using Laplace transform. {eq}\frac{d^2y}{dt^2} + 2\frac{dy}{dt} + y = e^{-t} {/eq} {eq}y(0) = 0 \\ y'(0) = 0 {/eq} Forward and Inverse Laplace Transform: The Laplace transform and the inverse La...
In this paper, we discussed about polynomial integral transform for solving differential equations and also we use Laplace transform polynomial integral transform solving differential equations with a little effort. Here the integral transform entails the function as its kernel. The Cauchy-Euler method ...
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Laplace Transform of a function {eq}f(t) {/eq} is the function {eq}F(s) {/eq} defined by {eq}\displaystyle F(s)=\mathcal{L}(f(t))=\int_{0}^{\infty}f(t)e^{-st}dt. {/eq} Applying the Laplace transform to a constant-coefficient linear diff...
In this paper we present a new technological approach to solve Ordinary differential equation. The application of MATLAB to compute and visualize the Laplace transforms is also discussed.doi:10.2671...
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Laplace transforms, Ordinary differential equation (ODE), MATLAB Abstract Laplace transform is a very powerful mathematical tool applied in various areas of engineering and science. With the increasing complexity of engineering problems, Laplace transforms help in solving complex problems with a very sim...
This article proposes the application of Laplace transform–homotopy perturbation method with variable coefficients, in order to find analytical approximate solutions for nonlinear differential equations with variable coefficients. As case study, we present the oxygen diffusion problem in a spherical cell inc...