AUTHOR(S): Jacob Manale
|
TITLE |
![]() |
ABSTRACT Euler introduced the formula y=expβ‘(Οx) 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{expβ‘γ(Ο[x+Ο])-expβ‘(-Ο[x+Ο]) γ}/(2 Ο), or simply y=a sinβ‘γ(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 Eulerβs Formula for Solving ODEs. International Journal of Mathematical and Computational Methods, 5, 1-3 |
|