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AUTHOR(S): Jacob Manale
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ABSTRACT Euler introduced the formula y=exp(ωx) 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〖(ω[x+ϕ])-exp(-ω[x+ϕ]) 〗}/(2 ω), or simply y=a sin〖(iω[x+ϕ])/(i ω). |
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KEYWORDS Ordinary Differential Equations, Partial Differential Equations, Linear Algebra, Complex Analysis |
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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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