A Formula for Particular Solutions Of Inhomogeneous Linear Ordinary Differential Equations of Fourth Order/n As I have shown earlier in [6] and [7], a particular solution for inhomogeneous linear second and third order ordinary differential equations may generally be determined. Applying what was determined from [6] and [7], and following by example a particular solution formula for fourth order may be obtained. As I have shown earlier in [6] and [7], a particular solution for inhomogeneous linear second and third order ordinary differential equations may be determined. Reference [6] contains two examples in verification. Reference [7] contains four examples in verification. The above process may be economized by re-using the analysis for 0 & yh as was used for W & yp , but for clarity in the first iterations each was isolated and treated separately. This process may be applied to the fourth order, then the fifth, and so on, yielding an algorithm for a particular solution for arbitrary order. This time, starting with a general n-th order approach along the same lines as the general reduction of order analysis. And, so, finally, the fourth order particular solution formula may be written as shown. Following this fourth order particular solution formula are two worked out examples. My arbitrary order formula book is now available on kindle. References [1] Kamke, E.; Differentialgleichungen LÅsungsmethoden Und LÅsungen, 3rd Ed., Chelsea Publishing Company, New York, N. Y.; 1959. [2] Nagle, R.K. , & Saff, E.B.; Fundamentals of Differential Equations and Boundary Value Problems; Addison Wesley Publishing Company, Inc.; Reading, MA; 1994. [3] Nagle, R.K. , & Saff, E.B., & Snider, A.D.; Fundamentals of Differential Equations, 5th Ed.; Addison Wesley Longman, Inc.; Reading, MA; 2000. [4] Polyanin, Andrei D. & Zaitsev, Valentin F.; Handbook of Exact Solutions for Ordinary Differential Equations, 2nd. Ed.; Chapman & Hall/CRC; New York, NY; 2003. [5] Zill, Dennis G.; A First Course in Differential Equations with Applications, 4th Ed.; PWS-KENT Publishing Company; Boston, MA; 1989. [6] Cassano, Claude M.; SciVee: DOI: 10.4016/28294.01 , http://www.scivee.tv/node/28294 ; http://www.dnatube.com/video/6899/A-Particular-Solutions-Inhomogeneous-2nd-Order-ODE-Formula [7] Cassano, Claude M.; http://www.dnatube.com/video/6967/A-Particular-Solutions-Inhomogeneous-3rd-Order-ODE-Formula My arbitrary order formula book is now available on kindle. As always: All my books are available on Kindle in digital format at amazon.com, and links to all my books may be found at the following websites https://sites.google.com/site/themathematicalnatureofreality/ https://sites.google.com/site/themathematicalnatureofreality/config/pagetemplates/books

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Tags: differential equation particular solution fourth order

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