![]() It imposes the condition that y cannot have higher index terms such as y 2, y 3 ,… and multiples of derivatives such as Suppose that f: X→Y and f(x)=y, a differential equation without nonlinear terms of the unknown function y and its derivatives is known as a linear differential equation. It is important to identify the difference between linear and nonlinear differential equations. Linear and nonlinear is one such categorization. Therefore, for easier identification differential equations are categorized by their mathematical behaviour. However, there are ones that we can solve, but may look alike and confusing. Resulting equations from a specific application of calculus may be very complex and sometimes not solvable. In fact, until calculus became an established theory, proper mathematical tools were unavailable to analyze the interesting problems in the nature. ![]() Differential equations are at the heart of every model we develop to explain any scenario or event in the world whether it is in physics, engineering, chemistry, statistics, financial analysis, or biology (the list is endless). Differential equations are of great importance in mathematics because of their range of applications. Since the development of calculus in the 18th century by the mathematicians like Newton and Leibnitz, differential equation has played an important role in the story of mathematics. The scope of this article is to explain what is linear differential equation, what is nonlinear differential equation, and what is the difference between linear and nonlinear differential equations. A differential equation can be either linear or non-linear. Linear vs Nonlinear Differential EquationsĪn equation containing at least one differential coefficient or derivative of an unknown variable is known as a differential equation.
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