<![CDATA[There are many problems in nature whose solutions are obtained through mathematical concepts. One of the most common mathematical concepts is a mathematical concept that is classified under initial value problems, such as a system of linear ordinary differential equations equipped with initial values. One tool that can solve the initial value problem is the Sawi transformation. This article describes the study of the initial value problem as a system of linear ordinary differential equations and its solution using the Sawi transformation. In addition, as part of applying the resulting theory, 2 (two) case examples are given (a first-order chemical reaction system with three certain chemicals and a mass-spring system with forced motion) to be solved using the Sawi transformation. So that problem solving can be interpreted and easily understood, in the 2 (two) case studies discussed and focused on the concentration of the chemical reactants, simulations were carried out for several different initial values and reaction rate constants. Compared to other methods (Laplace transform), the results obtained from using the Sawi transformation for the cases discussed show that the analytical solutions for the selected initial values have similar solutions.]]>
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