Applications of First-Order Differential Equation
Numerous disciplines, including physics, engineering, biology, economics, and more, first-order differential equations are used. Among other things, they are used to simulate phenomena like fluid dynamics, electrical circuits, population dynamics, and chemical reactions. Various applications of the first-order differential equation are:
- Used in Newton’s Law of Cooling
- Used in Orthogonal Trajectories
- Used in Falling Body Problems
- Used in Dilution Problems
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First Order Differential Equation
A first-order differential equation is a type of differential equation that involves derivatives of the first degree (first derivatives) of a function. It does not involve higher derivatives. It can generally be expressed in the form: dy/dx = f(x, y). Here, y is a function of x, and f(x, y) is a function that involves x and y.
It defined by an equation dy/dx = f (x, y) where x and y are two variables and f(x, y) are two functions. It is defined as a region in the xy plane. These types of equations have only the first derivative dy/dx so that the equation is of the first order and no higher-order derivatives exist.
Differential equations of first order is written as;
y’ = f (x, y)
(d/dx)y = f (x, y)
Let’s learn more about First-order Differential Equations, types, and examples of First-order Differential equations in detail below.
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