First Order Differential Equations In “real-world,” there are many physical quantities that can be represented by functions involving only one of the four variables e.g., (x, y, z, t) Equations involving highest order derivatives of order one = 1st order differential equations Examples: Its applications are common to find in the field of engineering, physics etc. In this article, we will learn about various applications in real life and in mathematics along with its definition and its types. Here, we look at how this works for systems of an object with mass attached to a vertical … 17.3: Applications of Second-Order Differential Equations - Mathematics LibreTexts MOTIVATING EXAMPLES Differential equations have wide applications in various engineering and science disciplines. Differential equations involve the derivatives of a function or a set of functions . Application 2 : Exponential Decay - Radioactive Material Let M(t) be the amount of a product that decreases with time t and the rate of decrease is proportional to the amount M as follows d M / d t = - k M where d M / d t is the first derivative of M, k > 0 and t is the time. Scond-order linear differential equations are used to model many situations in physics and engineering. 3 Applications of Di erential Equations Di erential equations are absolutely fundamental to modern science and engineering. The laws of the Natural and Physical world are usually written and modeled in the form of differential equations . Differential Equations Solve the above first order differential equation to obtain