A Compendium on Nonlinear Ordinary Differential Equations

✍ Scribed by P. L. Sachdev

• Publisher: John Wiley & Sons. Inc.
• Year: 1997
• Tongue: English
• Leaves: 934
• Category: Library

✦ Synopsis

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."

✦ Table of Contents

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(omegax + delta)
2.47 y" + ay' + g(x, y) = a sin(omegax + delta)
2.48 y" + f(y, y') = a sin(omegax + delta)
2.49 y" + g(x, y, y') = p(x), p periodic
2.50 y'[i] = fi, f[i] polynomial in y[1],y[2]
2.51 y'[i] = fi, f[i] not polynomial in y[1],y[2]
2.52 hiy'[i] = fi (i =1,2), f[i] polynomial in y[i]
2.53 hi*y'[i] = fi (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] = f1, y"[2]=f2
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] = f1, y"[2]=f2
4.10 y"[i] + gi = fi, (i = 1,2); g[i] linear in y[i]
4.11 y"[i] + gi = fi, (i = 1,2); g[i] not linear in y[i]
4.12 hiy"[i] + gi = fi, (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