# Laplace Transform Differential Equations in MATLAB Programming

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The Laplace transform of a function f(t) is

Laplace transforms are handy solutions of differential equations when the transforms of the forcing functions are known and can easily be converted with minimal modification. Typically, these include sinusoidal forcing functions, making this method ideal for the study of linear systems.

MATLAB Symbolic workflows retain calculations in the natural symbolic form instead of numeric form. This approach helps to understand the properties of the solution and use exact symbolic values. User should substitute numbers in place of symbolic variables only when he/she require a numeric result or cannot continue symbolically. These are basic steps in for solving differential equations

•   Declare equations.

•   Solve equations.

•   Substitute values.

•   Plot results.

•   Analyze results.

MATLAB presents several tools for modeling linear systems. These tools can be used to solve differential equations arising in various different models, and to show the input-output relations. This laplace transform differential equation will also covers system modeling using commands such as sys and tf, advanced usage of Simulink in laboratory measurement, and modeling tied systems using numerical methods. A simple search for Modeling Dynamical Systems Using Simulink points can result into several interesting introductory articles on MATLABâ€™s true power in the process of solving differential equation using Laplace.

MATLAB has large number of powerful features for solving differential equations of all types. This section will explore some of these features for the CCLODE forms. The approach here will be with the help of the Symbolic Math Toolbox. The result obtained will be in the form of the function and it may be readily plotted with MATLAB. Here is an example.

Representative CCLODE Form