In mathematics, the exponential response formula (ERF), also known as exponential response and complex replacement, is a method used to find a particular solution of a non-homogeneous linear ordinary differential equation of any order.[1][2] The exponential response formula is applicable to non-homogeneous linear ordinary differential equations with constant coefficients if the function is polynomial, sinusoidal, exponential or the combination of the three.[2] The general solution of a non-homogeneous linear ordinary differential equation is a superposition of the general solution of the associated homogeneous ODE and a particular solution to the non-homogeneous ODE.[1]
Alternative methods for solving ordinary differential equations of higher order are method of undetermined coefficients and method of variation of parameters.
^ abMiller, Haynes; Mattuck, Arthur (June 2004), Differential Equations, vol. IMSCP-MD5-9ca77abee86dc4bbaef9e2d6b157eaa9, pp. 50–56, hdl:1721.1/34888
^ abWirkus, Stephen A.; Swift, Randal J.; Szypowski, Ryan S. (2016), A Course in Differential Equations with Boundary Value Problems, Second Edition, Textbooks in Mathematics (2nd ed.), Chapman and Hall/CRC, pp. 230–238, ISBN 978-1498736053
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