THEORY AND PROBLEMS OF
DIFFERENTIAL EQUATIONS

The book includs 560 completely solved problems.

Contents:

1. Origin of differential equations

2. Solutions of differential equations

3. Equations of first order and first degree

4. Equations of first order and first degree – Variables separable and reduction to variables separable

5. Equations of first order and first degree – Exact equations and reduction to exact equations

6. Equations of first order and first degree – Linear equations and those reducible to that form

7. Geometric applications

8. Physical applications

9. Equations of first order and higher degree

10. Singular solutions – Extraneous loci

11. Applications of first order and higher degree equations

12. Linear equations of order n

13. Homogeneous linear equations with constant coefficients

14. Linear equations with constant coefficients

15. Linear equations with constant coefficients – Variation of parameters, undetermined coefficients

16. Linear equations with constant coefficients – Short method

17. Linear equations with constant coefficients – The Cauchy and Legendre linear equations

18. Linear equations with constant coefficients – Equations of the second order

19. Linear equations with constant coefficients – Miscellaneous types

20. Applications of linear equations

21. Systems of simultaneous linear equations

22. Total differential equations

23. Applications of total and simultaneous equations

24. Numerical approximations to solutions

25. Integration is series

26. Integration is series

27. The Legendre, Bessel, and Gauss equations

28. Partial differential equations

29. Linear partial differential equations of order one

30. Non-linear partial differential equations of order one

31. Homogeneous partial differential equations of higher order with constant coefficients

32. Non-homogeneous linear equations with constant coefficients

33. Partial differential equations of order two with variable coefficients