First-Order Linear Differential Equations
Chapter
First Online:
Abstract
Consider the first-order linear differential equation \(y'+p(t)y~=~q(t),~~~'=\frac{d~}{dt}\) where the functions p and q are continuous in an open interval \(I=(\alpha ,\beta )\) [1]. We can find the general solution of (1.1) in terms of the known functions p and q by multiplying both sides of (1.1) by an integrating factor \(e^{P(t)}\), where P(t) is a function such that \(P'(t)=p(t)\).
References
- 1.R.P. Agarwal, D. O’Regan, An Introduction to Ordinary Differential Equations (Springer, New York, 2008) CrossRefGoogle Scholar
- 2.H. Bradner, R.S. Mackay, Bull. Math. Biophys. 25, 251–272 (1963)Google Scholar
- 3.D.E. Caldwell, Biochemical Engineering V, Annals of the New York Academy of Sciences, vol. 56 (1987), pp. 274–280Google Scholar
- 4.J.L. Kulp, L.E. Tryin, W.R. Eckelman, W.A. Snell, Science 116, 409–414 (1952)CrossRefGoogle Scholar
- 5.L.S. Lai, S.T. Chou, W.W. Chao, J. Agric. Food Chem. 49, 963–968 (2001)CrossRefGoogle Scholar
- 6.J.L. Lebowitz, C.O. Lee, P.B. Linhart, Bell J. Econ. 7, 463–477 (1976)CrossRefGoogle Scholar
- 7.W.F. Libby, Radiocarbon Dating, 2nd edn. (University of Chicago Press, Chicago, 1955)Google Scholar
- 8.N. Rashevsky, Mathematical Biophysics, vol. 1 (Dover Publications, New York, 1960)zbMATHGoogle Scholar
- 9.L. Southwick, S. Zionts, Oper. Res. 22, 1156–1174 (1974)CrossRefGoogle Scholar
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