Integrating factors and first integrals of a class of third order differential equations. (English) Zbl 1386.34003
Summary: The principle of finding an integrating factor for a none exact differential equations is extended to a class of third order differential equations. If the third order equation is not exact, under certain conditions, an integrating factor exists which transforms it to an exact one. Hence, it can be reduced into a second order differential equation. In this paper, we give explicit forms for certain integrating factors of a class of the third order differential equations.
MSC:
| 34A05 | Explicit solutions, first integrals of ordinary differential equations |
| 34A25 | Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. |
| 34A30 | Linear ordinary differential equations and systems |
Keywords:
third order differential equation; exact differential equations; none exact differential equations; integrating factor; first integralsReferences:
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