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A Solution Manual For
A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983

Nasser M. Abbasi

May 15, 2024   Compiled on May 15, 2024 at 5:59am

1 Section 1. Basic concepts and definitions. Exercises page 18
2 Section 2. The method of isoclines. Exercises page 27
3 Section 3. The method of successive approximation. Exercises page 31
4 Section 4. Equations with variables separable and equations reducible to them. Exercises page 38
5 Section 5. Homogeneous equations. Exercises page 44
6 Section 6. Linear equations of the first order. The Bernoulli equation. Exercises page 54
7 Section 7, Total differential equations. The integrating factor. Exercises page 61
8 Section 8. First order not solved for the derivative. Exercises page 67
9 Section 8.3. The Lagrange and Clairaut equations. Exercises page 72
10 Section 9. The Riccati equation. Exercises page 75
11 Section 11. Singular solutions of differential equations. Exercises page 92
12 Section 12. Miscellaneous problems. Exercises page 93
13 Chapter 2 (Higher order ODE’s). Section 13. Basic concepts and definitions. Exercises page 98
14 Chapter 2 (Higher order ODE’s). Section 14. Differential equations admitting of depression of their order. Exercises page 107
15 Chapter 2 (Higher order ODE’s). Section 15.2 Homogeneous differential equations with constant coefficients. Exercises page 121
16 Chapter 2 (Higher order ODE’s). Section 15.3 Nonhomogeneous linear equations with constant coefficients. Trial and error method. Exercises page 132
17 Chapter 2 (Higher order ODE’s). Section 15.3 Nonhomogeneous linear equations with constant coefficients. Superposition principle. Exercises page 137
18 Chapter 2 (Higher order ODE’s). Section 15.3 Nonhomogeneous linear equations with constant coefficients. Initial value problem. Exercises page 140
19 Chapter 2 (Higher order ODE’s). Section 15.4 Nonhomogeneous linear equations with constant coefficients. The Euler equations. Exercises page 143
20 Chapter 2 (Higher order ODE’s). Section 15.5 Linear equations with variable coefficients. The Lagrange method. Exercises page 148
21 Chapter 2 (Higher order ODE’s). Section 16. The method of isoclines for differential equations of the second order. Exercises page 158
22 Chapter 2 (Higher order ODE’s). Section 17. Boundary value problems. Exercises page 163
23 Chapter 2 (Higher order ODE’s). Section 18.1 Integration of differential equation in series. Power series. Exercises page 171
24 Chapter 2 (Higher order ODE’s). Section 18.2. Expanding a solution in generalized power series. Bessels equation. Exercises page 177
25 Chapter 2 (Higher order ODE’s). Section 18.3. Finding periodic solutions of linear differential equations. Exercises page 187
26 Chapter 3 (Systems of differential equations). Section 19. Basic concepts and definitions. Exercises page 199
27 Chapter 3 (Systems of differential equations). Section 20. The method of elimination. Exercises page 212
28 Chapter 3 (Systems of differential equations). Section 21. Finding integrable combinations. Exercises page 219
29 Chapter 3 (Systems of differential equations). Section 22. Integration of homogeneous linear systems with constant coefficients. Eulers method. Exercises page 230
30 Chapter 3 (Systems of differential equations). Section 23. Methods of integrating nonhomogeneous linear systems with constant coefficients. Exercises page 234
31 Chapter 3 (Systems of differential equations). Section 23.2 The method of undetermined coefficients. Exercises page 239
32 Chapter 3 (Systems of differential equations). Section 23.3 dAlemberts method. Exercises page 243
33 Chapter 3. Section 24.2. Solving the Cauchy problem for linear differential equation with constant coefficients. Exercises page 249