### ME003/MA221: Differential Equations

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Differential equations are, in addition to a topic of study in mathematics, the main language in which the laws and phenomena of science are expressed.  In its most basic sense, a differential equation is an expression that describes how a system changes from one moment of time to another, or from one point in space to another.  When working with differential equations, the ultimate goal is to move from a microscopic view of relevant physics to a macroscopic view of the behavior of a system as a whole. Let’s look at a simple differential equation.  From previous math and physics courses, we know that a car that is constantly accelerating in the x-direction, for example, obeys the equation d2x/dt2 = a, where a is the applied acceleration.  This equation has two derivations with respect to time, so it is a second-order differential equation; because it has derivations with respect to only one variable (in this example, time), it is known as an  ordinary differential equation, or an ODE. Let’s say t…

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