# Book:E.L. Ince/Integration of Ordinary Differential Equations/Seventh Edition

## E.L. Ince: Integration of Ordinary Differential Equations (7th Edition)

Published $\text {1956}$, Oliver and Boyd Ltd.

### Contents

Preface (May 1939)
Preface to the Second Edition (April 1943) (A.C. Aitken and D.E. Rutherford)
CHAPTER $\text {I}$: EQUATIONS OF THE FIRST ORDER AND DEGREE
1. Definitions
2. Integration
3. Separation of Variables
4. The Homogeneous Type
5. The Equation with Linear Coefficients
6. Exact Equations
7. Integrating Factors
8. The Quotient of Two Integrating Factors
9. Special Types of Integrating Factor
10. The Linear Equation
11. The Bernoulli Equation
12. The Riccati Equation
13. Change of Variable
CHAPTER $\text {II}$: INTEGRAL CURVES
14. Families of Plane Curves
15. Trajectories
16. Level Lines and Lines of Slope on a Surface
17. Singular Points
CHAPTER $\text {III}$: EQUATIONS OF HIGHER DEGREE
18. The General Integral
19. The Clairaut Equation
20. Generalisation - the d'Alembert Equation
21. Further Generalisation
22. Equations with One Variable Missing
23. Homogeneous Equations
24. Geometrical Interpretation of a Differential Equation
25. Cusp on the Integral Curve
26. Envelope of Integral Curves
27. Equation of the Second Degree
CHAPTER $\text {IV}$: EQUATIONS OF THE SECOND AND HIGHER ORDERS
28. Reduction of the Order of an Equation
29. Equations that do not Involve $y$
30. Equations that do not Involve $x$
31. First Homogeneous Type
32. Second Homogeneous Type
33. Third Homogeneous Type
34. A Special Case of Homogeneity
35. First Integral
36. Problems Involving Curvature
CHAPTER $\text {V}$: LINEAR EQUATIONS
37. Form of the General Integral
38. Depression of the Order
39. Reduced Equation with Constant Coefficients
40. Properties of the Operator $\map F D$
41. Pairs of Conjugate Factors
42. Repeated Real Factors
43. Repeated Complex Factors
44. Inverse Operators
45. Inverse Operators Relative to a Periodic Function
46. Development of an Inverse Operator
48. The Euler Linear Equation
49. The Laplace Linear Equation
50. Variation of Parameters
51. Linear Systems with Constant Coefficients
CHAPTER $\text {VI}$: SOLUTION IN SERIES
52. Solution Developed as a Taylor Series
53. Regular Singularity
54. The Hypergeometric Equation
55. The Legendre Equation and the Function $\map {P_n} x$
56. Solution for Large Values of $\size x$
57. The Bessel Equation and the Function $\map {J_n} x$
58. The Function $\map {Y_n} x$
EXAMPLES
SOLUTIONS
INDEX

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