home
up
PDF (letter size)
PDF (legal size)

Computer Algebra report

Solved differential equations

from selected books

Step by step solutions

Nasser M. Abbasi

November 24, 2020   Compiled on November 24, 2020 at 5:57am

pict

pict

pict

pict

pict

pict

pict

pict

pict

pict

pict

pict

pict

pict

pict

pict

pict

pict

pict

pict

pict

pict

pict

1 Introduction
 1.1 Text books used
 1.2 About the program
 1.3 Summary of results
2 Differential equations and linear algebra, 3rd ed., Edwards and Penney
 2.1 Section 1.2. Integrals as general and particular solutions. Page 16
 2.2 Section 1.3. Slope fields and solution curves. Page 26
 2.3 Section 1.4. Separable equations. Page 43
 2.4 Section 1.5. Linear first order equations. Page 56
 2.5 Section 1.6, Substitution methods and exact equations. Page 74
 2.6 Chapter 1 review problems. Page 78
 2.7 Section 5.1, second order linear equations. Page 299
 2.8 Section 5.2, second order linear equations. Page 311
 2.9 Section 5.3, second order linear equations. Page 323
 2.10 Section 5.4, Mechanical Vibrations. Page 337
 2.11 Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
 2.12 Section 5.6, Forced Oscillations and Resonance. Page 362
 2.13 Section 7.2, Matrices and Linear systems. Page 417
3 Differential equations and linear algebra, 4th ed., Edwards and Penney
 3.1 Section 5.2, Higher-Order Linear Differential Equations. General solutions of Linear Equations. Page 288
 3.2 Section 5.3, Higher-Order Linear Differential Equations. Homogeneous Equations with Constant Coefficients. Page 300
 3.3 Section 6.1, Introduction to Eigenvalues, Eigenvalues and Eigenvectors. Page 346
 3.4 Section 6.2, Diagonalization of Matrices, Eigenvalues and Eigenvectors. Page 354
 3.5 Section 7.2, Matrices and Linear systems. Page 384
 3.6 Section 7.3, The eigenvalue method for linear systems. Page 395
 3.7 Section 7.6, Multiple Eigenvalue Solutions. Examples. Page 437
 3.8 Section 7.6, Multiple Eigenvalue Solutions. Page 451
4 Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
 4.1 Section 2.1. Page 40
 4.2 Section 2.2. Page 48
 4.3 Section 2.4. Page 76
 4.4 Section 2.5. Page 88
 4.5 Section 2.6. Page 100
 4.6 Miscellaneous problems, end of chapter 2. Page 133
 4.7 Chapter 3, Second order linear equations, 3.1 Homogeneous Equations with Constant Coefficients, page 144
 4.8 Chapter 3, Second order linear equations, 3.3 Complex Roots of the Characteristic Equation , page 164
 4.9 Chapter 3, Second order linear equations, 3.4 Repeated roots, reduction of order , page 172
 4.10 Chapter 3, Second order linear equations, section 3.6, Variation of Parameters. page 190
 4.11 Chapter 3, Second order linear equations, 3.7 Mechanical and Electrical Vibrations. page 203
 4.12 Chapter 3, Second order linear equations, 3.7 Forced Vibrations. page 217
 4.13 Chapter 7.5, Homogeneous Linear Systems with Constant Coefficients. page 407
 4.14 Chapter 7.6, Complex Eigenvalues. page 417
 4.15 Chapter 7.8, Repeated Eigenvalues. page 436
 4.16 Chapter 7.9, Nonhomogeneous Linear Systems. page 447
 4.17 Chapter 9.1, The Phase Plane: Linear Systems. page 505
 4.18 Chapter 9.2, Autonomous Systems and Stability. page 517
5 Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
 5.1 Section 1.2 Page 14
 5.2 Section 2.1 Page 34
 5.3 Section 2.2 Page 47
 5.4 Section 2.3 Page 55
 5.5 Section 2.4 Page 57
 5.6 Section 2.5 Page 73
 5.7 Section 2.6 Page 91
 5.8 Chapter 5 linear second order equations. Section 5.1 Homogeneous linear equations. Page 203
 5.9 Chapter 5 linear second order equations. Section 5.6 Reduction or order. Page 253
 5.10 Chapter 5 linear second order equations. Section 5.7 Variation of Parameters. Page 262
 5.11 Chapter 9 Introduction to Linear Higher Order Equations. Section 9.1. Page 471
 5.12 Chapter 9 Introduction to Linear Higher Order Equations. Section 9.2. constant coefficient. Page 483
 5.13 Chapter 9 Introduction to Linear Higher Order Equations. Section 9.3. Undetermined Coefficients for Higher Order Equations. Page 495
 5.14 Chapter 9 Introduction to Linear Higher Order Equations. Section 9.4. Variation of Parameters for Higher Order Equations. Page 503
 5.15 Chapter 10 Linear system of Differential equations. Section 10.4, constant coefficient homogeneous system. Page 540
 5.16 Chapter 10 Linear system of Differential equations. Section 10.5, constant coefficient homogeneous system II. Page 555
 5.17 Chapter 10 Linear system of Differential equations. Section 10.6, constant coefficient homogeneous system III. Page 566
6 Differential equations and their applications, 3rd ed., M. Braun
 6.1 Section 1.2. Page 6
 6.2 Section 1.2. Page 9
 6.3 Section 1.4. Page 24
 6.4 Section 1.9. Page 66
 6.5 Section 1.10. Page 80
 6.6 Section 2.1, second order linear differential equations. Page 134
 6.7 Section 2.2, linear equations with constant coefficients. Page 138
 6.8 Section 2.2.1, Complex roots. Page 141
 6.9 Section 2.2.2, Equal roots, reduction of order. Page 147
 6.10 Section 2.4, The method of variation of parameters. Page 154
 6.11 Section 2.6, Mechanical Vibrations. Page 171
 6.12 Section 2.8, Series solutions. Page 195
 6.13 Section 2.8.1, Singular points, Euler equations. Page 201
 6.14 Section 2.8.2, Regular singular points, the method of Frobenius. Page 214
7 Differential equations and their applications, 4th ed., M. Braun
 7.1 Section 3.8, Systems of differential equations. The eigenva1ue-eigenvector method. Page 339
 7.2 Section 3.9, Systems of differential equations. Complex roots. Page 344
 7.3 Section 3.10, Systems of differential equations. Equal roots. Page 352
 7.4 Section 3.12, Systems of differential equations. The nonhomogeneous equation. variation of parameters. Page 366
8 Differential Gleichungen, Kamke, 3rd ed
 8.1 section 1.0
9 Differential Equations, Nelson, Folley, Coral, 3rd ed, 1964
 9.1 Exercis 5, page 21
 9.2 Exercis 6, page 25
10 Elementary Differential Equations, Martin, Reissner, 2nd ed, 1961
 10.1 Exercis 2, page 5
11 Ordinary Differential Equations, Robert H. Martin, 1983
 11.1 Problem 1.1-2, page 6
 11.2 Problem 1.1-3, page 6
 11.3 Problem 1.1-4, page 7
 11.4 Problem 1.1-5, page 7
 11.5 Problem 1.1-6, page 7
 11.6 Problem 1.2-1, page 12
 11.7 Problem 1.2-2, page 12
 11.8 Problem 1.2-3, page 12
12 Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition, 2002
 12.1 Chapter 14, First order ordinary differential equations. 14.4 Exercises, page 490
 12.2 Chapter 15, Higher order ordinary differential equations. 15.4 Exercises, page 523
13 Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
 13.1 1.4, page 36
 13.2 1.6, page 50
 13.3 1.8, page 68
14 Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
 14.1 Chapter 9, Linear differential equations of order n. Section 8.1, General Theory for Linear Differential Equations. page 502
15 Differential equations, Shepley L. Ross, 1964
 15.1 2.4, page 55
16 Applied Differential equations, N Curle, 1971
 16.1 Examples, page 35
17 Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
 17.1 Exercises, page 14
18 Elementary Differential equations, Chaundy, 1969
 18.1 Exercises 3, page 60
19 Advanced Mathematica, Book2, Perkin and Perkin, 1992
 19.1 Chapter 11.3, page 316
20 Differential equations with applications and historial notes, George F. Simmons, 1971
 20.1 Chapter 2, section 7, page 37
 20.2 Chapter 2, section 8, page 41
 20.3 Chapter 2, section 10, page 47
 20.4 Chapter 2, section 11, page 49
 20.5 Chapter 2, End of chapter, page 61
21 An introduction to the solution and applications of differential equations, J.W. Searl, 1966
 21.1 Chapter 4, Ex. 4.1
 21.2 Chapter 4, Ex. 4.2
22 Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
 22.1 Chapter 2
23 Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
 23.1 Various 1
 23.2 Various 2
 23.3 Various 3
 23.4 Various 4
 23.5 Various 5
 23.6 Various 6
 23.7 Various 7
 23.8 Various 8
 23.9 Various 9
 23.10 Various 10
 23.11 Various 11
 23.12 Various 12
 23.13 Various 13
 23.14 Various 14
 23.15 Various 15
 23.16 Various 16
 23.17 Various 17
 23.18 Various 18
 23.19 Various 19
 23.20 Various 20
 23.21 Various 21
 23.22 Various 22
 23.23 Various 23
 23.24 Various 24
 23.25 Various 25
 23.26 Various 26
 23.27 Various 27
 23.28 Various 28
 23.29 Various 29
 23.30 Various 30
 23.31 Various 31
 23.32 Various 32
 23.33 Various 33
 23.34 Various 34
 23.35 Various 35
 23.36 Various 36
 23.37 Various 37
24 Differential and integral calculus, vol II By N. Piskunov. 1974
 24.1 Chapter 1
25 Differential Equations, By George Boole F.R.S. 1865
 25.1 Chapter 2
 25.2 Chapter 3
 25.3 Chapter 4
 25.4 Chapter 5
 25.5 Chapter 6
 25.6 Chapter 7
26 Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
 26.1 Chapter 2. Special types of differential equations of the first kind. Lesson 7
 26.2 Chapter 2. Special types of differential equations of the first kind. Lesson 8
 26.3 Chapter 2. Special types of differential equations of the first kind. Lesson 9
 26.4 Chapter 2. Special types of differential equations of the first kind. Lesson 10
 26.5 Chapter 2. Special types of differential equations of the first kind. Lesson 11, Bernoulli Equations
 26.6 Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous Methods
 26.7 Chapter 4. Higher order linear differential equations. Lesson 20. Constant coefficients
 26.8 Chapter 4. Higher order linear differential equations. Lesson 21. Undetermined Coefficients
 26.9 Chapter 4. Higher order linear differential equations. Lesson 22. Variation of Parameters
 26.10 Chapter 8. Special second order equations. Lesson 35. Independent variable x absent
27 Differential Gleichungen, Kamke, 3rd ed, Abel ODEs
 27.1 Abel ODE’s with constant invariant
28 Own collection of miscellaneous problems
 28.1 section 1.0