“Inexact differential equation”的意思、由来-开放百科全书

词条

Inexact differential equation

释义

Solution method
References
External links

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An inexact differential equation is a differential equation of the form (see also: inexact differential)

The solution to such equations came with the invention of the integrating factor by Leonhard Euler in 1739.^[1]

Solution method

In order to solve the equation, we need to transform it into an exact differential equation. In order to do that, we need to find an integrating factor to multiply the equation by. We'll start with the equation itself., so we get . We will require to satisfy . We get . After simplifying we get . Since this is a partial differential equation, it is mostly extremely hard to solve, however in most cases we will get either or , in which case we only need to find with a first-order linear differential equation or a separable differential equation, and as such either or .

References

1. ^{{Cite web|url=http://www.eoht.info/page/History+of+differential+equations|title=History of differential equations – Hmolpedia|website=www.eoht.info|access-date=2016-10-16}}

External links

A solution for an inexact differential equation from http://math.stackexchange.com/
a guide for non-partial inexact differential equations at SOS math

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