Jacob Manale



On Errors in Euler’s Formula for Solving ODEs

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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).


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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