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A Compendium on Nonlinear Ordinary Differential Equations

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From Introduction: "I do not recollect the mystical moment when the thought to prepare this compendium captured my imagination. It was not unnatural to conceive of it after I had completed my book Nonlinear Ordinary Differential Equations and Their Applications, since published by Marcel Dekker (1991), but I was only vaguely aware of the task ahead, and the enormity of the effort that would be demanded of me. As I plodded on, thumbing through literally hundreds of volumes of journals, hunting out useful, interesting, known and not-sowell- known equations, I realized that the volume I had envisioned as modest in size would grow and that it could never be exhaustive. However, the search continued and the material piled up. It took a relentless effort of five years to bring this work to its present stage of completion. I ransacked mathematics sections of many libraries: the Courant Institute, NYU, Rutgers, New Jersey Institute of Technology, St. Andrews (UK), TIFR and lIT, Bombay, and the Indian Institute of Science, Bangalore. Almost all journals in applied mathematics, physics, and engineering that deal with nonlinear phenomenon were browsed through. That explains the large size of the biblography and, of course, of the compendium itself. Yet it does not seem possible to exhaust all the equations, since new ones get added to the literature almost every day. The present collection should, nevertheless, meet the needs of a large majority of scientists, engineers, and applied mathematicians."

Author(s): P. L. Sachdev
Publisher: John Wiley & Sons. Inc.
Year: 1997

Language: English
Pages: IV; 918
City: New York

Title Page
Table of Contents
Preface
1 INTRODUCTION
1.1 Instructions to the User
2 SECOND ORDER EQUATIONS
2.1 y" + f(y) = 0, f(y) polynomial
2.2 y" + f(y) = 0, f(y) not polynomial
2.3 y" + g(x)h(y) = 0
2.4 y" + f(x, y) = 0, f(x, y) polynomial in y
2.5 y" + f(x, y) = 0, f(x, y) not polynomial in y
2.6 y" + f(x, y) = 0, f(x, y) general
2.7 y" + ay' + g(x,y) = 0
2.8 y" + ky'lx + g(x, y) = 0
2.9 y" + f(x)y' + g(x, y) = 0
2.10 y" + kyy' + g(x, y) = 0
2.11 y" + f (y) y' +9 (x, y) = 0, f (y) polynomial
2.12 y" + f(y)y' + g(x, y) = 0, f(y) not polynomial
2.13 y" + f(x, y)y' + g(x, y) = O
2.14 y" + ay'² + g(x, y)y' + h(x, y) = 0
2.15 y" + ky'² /y + g(x, y)y' + h(x, y) = 0
2.16 y" + f(y)y'² + g(x, y)y' + h(x, y) = 0
2.17 y" + f(x, y)y'² + g(x, y)y' + h(x, y) = 0
2.18 y" + f(y, y') = 0, f(y, y') cubic in y'
2.19 y" + f(x, y, y') = 0, f(x, y, y') cubic in y'
2.20 y" + f(y') + g(x, y) = O
2.21 y" + h(y)f(y') + g(x, y) = 0
2.22 y" + f(y,y') = O
2.23 y" + h(x)k(y)f(y') + g(x,y) = 0
2.24 y" + f(x, y, y') = 0
2.25 xy" + g(x, y, y') = O
2.26 x²y" + g(x, y, y') = 0
2.27 (f(x)y')' + g(x, y) = 0
2.28 f(x)y" + g(x, y, y') = 0
2.29 yy" + G(x, y, y') = 0
2.30 yy" + ky'² + g(x, y, y') = 0, k > 0, g linear in y'
2.31 yy" + ky'² + g(x, y, y') = 0, k < 0, g linear in y/
2.32 yy" + ky'² + g(x, y, y') = 0, k a general constant, g linear in y'
2.33 yy" + g(x, y, y') = 0
2.34 xyy" + g(x, y, y') = 0
2.35 x²yy" + g(x, y, y') = 0
2.36 f(x)yy" + g(x, y, y') = 0
2.37 f(y)y" + g(x, y, y') = 0, f(y) quadratic
2.38 f(y)y" + g(x, y, y') = 0, f(y) cubic
2.39 f(y)y" + g(x, y, y') = 0
2.40 h(x)f(y)y" + g(x, y, y') = 0
2.41 f(x, y)y" + g(x, y, y') = O
2.42 f(y, y')y" + g(x, y, y') = 0
2.43 f(x, y, y')y" + g(x, y, y') = 0
2.44 f(x, y, y', y") = 0, f polynomial in y"
2.45 f(x,y,y',y") = 0, f not polynomial in y"
2.46 y" + f(y) = a sin(omega*x + delta)
2.47 y" + ay' + g(x, y) = a sin(omega*x + delta)
2.48 y" + f(y, y') = a sin(omega*x + delta)
2.49 y" + g(x, y, y') = p(x), p periodic
2.50 y'[i] = f[i](x, y[i]), f[i] polynomial in y[1],y[2]
2.51 y'[i] = f[i](x, y[i]), f[i] not polynomial in y[1],y[2]
2.52 h[i](x,y[1],y[2])*y'[i] = f[i](x,y[1],y[2]) (i =1,2), f[i] polynomial in y[i]
2.53 h[i](x,y[1],y[2])*y'[i] = f[i](x,y[1],y[2]) (i =1,2), f[i] not polynomial in y[i]
3 THIRD ORDER EQUATIONS
3.1 y'" + f(y) = 0 and y"' + f(x,y) = 0
3.2 y'" + f(x, y)y' + g(x, y) = 0
3.3 y'" + f(x, y, y') = 0
3.4 y'" + ay" + !(y, y') = 0
3.5 y'" + ayy" + f(x, y, y') = 0
3.6 y'" + f(x, y, y')y" + g(x, y, y') = 0
3.7 y'" + f(x, y, y', y") = 0, f not linear in y"
3.8 f(x)y'" + g(x, y, y', y") = 0
3.9 f(x, y)y'" + g(x, y, y', y") = O
3.10 f(x, y, y', y")y'" + g(x, y, y', y") = 0
3.11 f(x, y, y', y", y'") = 0, f nonlinear in y'"
3.12 f(x,y,y',y",y'") =p(x), p periodic
3.13 y'[i] = f(y[i]); f[1], f[2], f[3] linear and quadratic in y[1],y[2], y[3]
3.14 y'[i] = f(y[i]); f[1], f[2], f[3] all quadratic in y[1],y[2], y[3]
3.15 y'[i] = f(y[i]); f[1], f[2], f[3] homogenous quadratic in y[1],y[2], y[3]
3.16 y'[i] = f(y[i]); f[1], f[2], f[3] polynomial in y[1],y[2], y[3]
3.17 y'[i] = f(y[i]); f[1], f[2], f[3] not polynomial in y[1],y[2], y[3]
3.18 y'[i] = f(x,y[i])
3.19 y'[1] = f[1](x,y[i]), y"[2]=f[2](x, y[i])
4 FOURTH ORDER EQUATIONS
4.1 y"" + f(x, y, y') = 0
4.2 y"" + ky" + f(x, y, y') = 0
4.3 y"" + ayy" + f(x, y, y') = 0
4.4 y"" + f(x, y, y', y") = 0
4.5 y"" + ayy'" + f(x, y, y', y") = 0
4.6 y"" + f(x,y,y',y",y'") = 0
4.7 f(x,y,y',y",y'")y"" + g(x,y,y',y",y'") = 0
4.8 y'[i] = f(x,y[i])
4.9 y"[1] = f[1](x,y[i]), y"[2]=f[2](x, y[i])
4.10 y"[i] + g[i](x,y[1],y[2],y'[1],y'[2]) = f[i](x,y[1],y[2]), (i = 1,2); g[i] linear in y[i]
4.11 y"[i] + g[i](x,y[1],y[2],y'[1],y'[2]) = f[i](x,y[1],y[2]), (i = 1,2); g[i] not linear in y[i]
4.12 h[i](x,y[1],y[2],y'[1],y'[2])y"[i] + g[i](x,y[1],y[2],y'[1],y'[2]) = f[i](x,y[1],y[2]), (i = 1,2)
5 FIFTH ORDER EQUATIONS
5.1 Fifth Order Single Equations
5.2 Fifth Order Systems
6 SIXTH ORDER EQUATIONS
6.1 Sixth and Specific Higher Order Single Equations
6.2 Sixth and Specific Higher Order System
N GENERAL ORDER EQUATIONS
N.1 General Order Single Equations
N.2 Systems of General Order
BIBLIOGRAPHY