Kelvin Differential Equation

The complex second-order ordinary differential equation

(1)

(Abramowitz and Stegun 1972, p. 379; Zwillinger 1997, p. 123), whose solutions can be given in terms of the Kelvin functions as

			(2)
			(3)
			(4)
			(5)

(Abramowitz and Stegun 1972, p. 379).

The general solution is

(6)

where  is a Bessel function of the first kind and  is a Bessel function of the second kind.

REFERENCES:

Abramowitz, M. and Stegun, I. A. (Eds.). "Kelvin Functions." §9.9 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 379-381, 1972.

Zwillinger, D. Handbook of Differential Equations, 3rd ed. Boston, MA: Academic Press, p. 123, 1997.