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Chapter 75
A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
75.1
Section 1. Basic concepts and definitions. Exercises page 18
75.2
Section 2. The method of isoclines. Exercises page 27
75.3
Section 3. The method of successive approximation. Exercises page 31
75.4
Section 4. Equations with variables separable and equations reducible to them. Exercises page 38
75.5
Section 5. Homogeneous equations. Exercises page 44
75.6
Section 6. Linear equations of the first order. The Bernoulli equation. Exercises page 54
75.7
Section 7, Total differential equations. The integrating factor. Exercises page 61
75.8
Section 8. First order not solved for the derivative. Exercises page 67
75.9
Section 8.3. The Lagrange and Clairaut equations. Exercises page 72
75.10
Section 9. The Riccati equation. Exercises page 75
75.11
Section 11. Singular solutions of differential equations. Exercises page 92
75.12
Section 12. Miscellaneous problems. Exercises page 93
75.13
Chapter 2 (Higher order ODEs). Section 13. Basic concepts and definitions. Exercises page 98
75.14
Chapter 2 (Higher order ODEs). Section 14. Differential equations admitting of depression of their order. Exercises page 107
75.15
Chapter 2 (Higher order ODEs). Section 15.2 Homogeneous differential equations with constant coefficients. Exercises page 121
75.16
Chapter 2 (Higher order ODEs). Section 15.3 Nonhomogeneous linear equations with constant coefficients. Trial and error method. Exercises page 132
75.17
Chapter 2 (Higher order ODEs). Section 15.3 Nonhomogeneous linear equations with constant coefficients. Superposition principle. Exercises page 137
75.18
Chapter 2 (Higher order ODEs). Section 15.3 Nonhomogeneous linear equations with constant coefficients. Initial value problem. Exercises page 140
75.19
Chapter 2 (Higher order ODEs). Section 15.4 Nonhomogeneous linear equations with constant coefficients. The Euler equations. Exercises page 143
75.20
Chapter 2 (Higher order ODEs). Section 15.5 Linear equations with variable coefficients. The Lagrange method. Exercises page 148
75.21
Chapter 2 (Higher order ODEs). Section 16. The method of isoclines for differential equations of the second order. Exercises page 158
75.22
Chapter 2 (Higher order ODEs). Section 17. Boundary value problems. Exercises page 163
75.23
Chapter 2 (Higher order ODEs). Section 18.1 Integration of differential equation in series. Power series. Exercises page 171
75.24
Chapter 2 (Higher order ODEs). Section 18.2. Expanding a solution in generalized power series. Bessels equation. Exercises page 177
75.25
Chapter 2 (Higher order ODEs). Section 18.3. Finding periodic solutions of linear differential equations. Exercises page 187
75.26
Chapter 3 (Systems of differential equations). Section 19. Basic concepts and definitions. Exercises page 199
75.27
Chapter 3 (Systems of differential equations). Section 20. The method of elimination. Exercises page 212
75.28
Chapter 3 (Systems of differential equations). Section 21. Finding integrable combinations. Exercises page 219
75.29
Chapter 3 (Systems of differential equations). Section 22. Integration of homogeneous linear systems with constant coefficients. Eulers method. Exercises page 230
75.30
Chapter 3 (Systems of differential equations). Section 23. Methods of integrating nonhomogeneous linear systems with constant coefficients. Exercises page 234
75.31
Chapter 3 (Systems of differential equations). Section 23.2 The method of undetermined coefficients. Exercises page 239
75.32
Chapter 3 (Systems of differential equations). Section 23.3 dAlemberts method. Exercises page 243
75.33
Chapter 3. Section 24.2. Solving the Cauchy problem for linear differential equation with constant coefficients. Exercises page 249
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