INTEGRATING FACTOR Meaning and
Definition
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An integrating factor is a mathematical concept used in the field of differential equations. In the context of differential equations, an integrating factor is a function multiplied to both sides of an equation to make it easier to solve.
Specifically, an integrating factor is a function that is multiplied to a given differential equation in order to make it exact or to simplify its solution. The concept is commonly used for linear first-order or homogeneous second-order differential equations.
For a linear first-order differential equation, multiplying both sides of the equation by an integrating factor can transform it into an exact equation, which can be solved more readily. The integrating factor depends on the differential equation itself and is often found by identifying a specific function that yields an exact equation when multiplied by the original equation.
Similarly, for homogeneous second-order differential equations, an integrating factor can be applied to transform the equation into a simpler form, often resulting in a separable equation that can be solved more easily.
In summary, an integrating factor is a function that is multiplied to a differential equation to aid in its solution. It can be used to make an equation exact or to simplify it, thereby facilitating the process of finding a solution.
Common Misspellings for INTEGRATING FACTOR
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Etymology of INTEGRATING FACTOR
The word "integrating factor" primarily comes from the field of mathematics, specifically in the context of differential equations.
The term "integrating" is derived from the Latin word "integrare", which means "to make whole or complete". In the context of mathematics, integration refers to the process of finding the antiderivative or integral of a function. This term is used because integrating factors are employed to complete the integration of certain types of differential equations.
The term "factor" refers to an element or quantity that contributes to a result or outcome. In the case of integrating factors, they are multiplicative factors used to transform a given differential equation into a form that allows for easier integration.
Combining both terms, the etymology of "integrating factor" suggests a factor or element that aids in completing the integration process or in making the equation whole.
