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AUTHOR(S):

Jacob Manale

 

TITLE

On Errors in Euler’s Formula for Solving ODEs

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ABSTRACT

Euler introduced the formula y=exp⁑(Ο‰x) for solving ODEs of the form Ay^''+By^'+Cy=0. It is now a procedure that can be found at the basis of numerous mathematical theories, and has countless applications in several fields. In this contribution, we demonstrate that this formula is invalid as a tool for solving such equations. We determine the correct one through quadrature, and establish it to be y=a{exp⁑〖(Ο‰[x+Ο•])-exp⁑(-Ο‰[x+Ο•]) γ€—}/(2 Ο‰), or simply y=a sin⁑〖(iΟ‰[x+Ο•])/(i Ο‰).

KEYWORDS

Ordinary Differential Equations, Partial Differential Equations, Linear Algebra, Complex Analysis

 

Cite this paper

Jacob Manale. (2020) On Errors in Euler’s Formula for Solving ODEs. International Journal of Mathematical and Computational Methods, 5, 1-3

 

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