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Differential Equations

In: Economic Analysis Through Mathematics

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  • Zrinka Lukač

    (University of Zagreb, Faculty of Economics & Business)

Abstract

In economic models, often it is important to know how the value of an economic variable changes over time. The relationship between variables is often described by a single equation or a system of equations that include the variables and also their derivatives. In the case when the value of these variables is observed in continuous time, we talk about differential equations. Differential equations are equations that relate the independent variable x and the unknown function y = y ( x ) $$y=y(x)$$ with the property that they contain at least one derivative of the function y or the differentials dx and dy. The order of the highest derivative (or differential) appearing in a given differential equation is called the order of that differential equation. In this chapter, we deal only with linear differential equations and show methods to solve them in the case of both the homogeneous and nonhomogeneous linear differential equations.

Suggested Citation

  • Zrinka Lukač, 2026. "Differential Equations," Springer Texts in Business and Economics, in: Economic Analysis Through Mathematics, chapter 21, pages 515-527, Springer.
    • Handle: RePEc:spr:sptchp:978-3-032-08812-3_21
    DOI: 10.1007/978-3-032-08812-3_21
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