A Particular Solutions Inhomogeneous Linear Second Order Ordinary Differential Equations Formula

A relatively simple formula is presented which allows a particular solution for an inhomogeneous second order linear ordinary differential equation to be written and evaluated immediately.
For second order linear ODEs this formula make the methods of undetermined coefficients and variation of parameters obsolete.
The proofs in more detail may be found in my book available in print and on Kindle in digital format at amazon.com ; and links to all my books may be found at:
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A Helmholtzian operator and electromagnetic-nuclear field

A Helmholtzian operator is a linear second order partial differential operator, typically in four independant variables; a generalization of the d'Alembertian operator where it's additional constant vanishes. When the time-independant version (in three independent (space) variables acting on a function or vector vanishes, the resulting equation is called the Helmholtz's equation. In four dimensions this equation is referred to as the Klein-Gordon equation (with imaginary constant).
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All my books are available at amazon.com in digital format on Kindle, and some in print; and links to all my books may be found at:
themathematicalnatureofreality:books

The d'Alembertian and Maxwell's equations

The d'Alembertian is a linear second order differential operator, typically in four independant variables. The time-independant version (in three independent (space) variables is called the Laplacian operator.
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All my books are available at amazon.com in digital format on Kindle, and some in print; and links to all my books may be found at:
themathematicalnatureofreality:books