Abstract
Certain nonlinear first-order differential equations can be reduced to linear equations by an appropriate change of variables [1, 2]. For example, it is always possible for the James (Jacob) Bernoulli’s (1654–1705) equation \(y'+p(t)y~=~q(t)y^n,~~~n\ne 0,~1.\) In (2.1), \(n=0\) and 1 are excluded because in these cases the Eq. (2.1) is obviously linear.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
R.P. Agarwal, D. O’Regan, An Introduction to Ordinary Differential Equations (Springer, New York, 2008)
R.P. Agarwal, D. O’Regan, Ordinary and Partial Differential Equations with Special Functions, Fourier Series and Boundary Value Problems (Springer, New York, 2009)
A.G.W. Cameron, Icarus 18, 407–450 (1973)
G. Cook, L. Stark, Bull. Math. Biophys. 29, 153–174 (1967)
H.V. Foerster, P.M. Mora, L.W. Amiot, Science 12, 1291–1295 (1960)
J.B.S. Haldane, Causes of Evolution (Cornell University Press, Ithaca, 1966)
D. Hamberg, Models of Economic Growth (Harper & Row, New York, 1971)
J.Z. Hearon, Bull. Math. Biophys. 17, 7–13 (1962)
W.J. Oomens, The Demand for Consumer Durables (Tilburg University Press, The Netherlands, 1976)
A. Rapoport, Bull. Math. Biophys. 14, 159–169 (1952)
J.J. Stoker, Water Waves (Interscience, New York, 1957)
L.L. Thurstone, J. Gen. Psychol. 3, 469–493 (1930)
D.G. Zill, A First Course in Differential Equations with Modeling Applications (Cengage Learning, Boston, 2016)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Agarwal, R.P., Hodis, S., O’Regan, D. (2019). Some First-Order Nonlinear Differential Equations. In: 500 Examples and Problems of Applied Differential Equations. Problem Books in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-26384-3_2
Download citation
DOI: https://doi.org/10.1007/978-3-030-26384-3_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-26383-6
Online ISBN: 978-3-030-26384-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)