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

Subject Matter

 * Ordinary Differential Equations

Contents

 * Preface (May 1939)
 * Preface to the Second Edition (April 1943) (A.C. Aitken and D.E. Rutherford)


 * CHAPTER 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 II: INTEGRAL CURVES
 * 14. Families of Plane Curves
 * 15. Trajectories
 * 16. Level Lines and Lines of Slope on a Surface
 * 17. Singular Points


 * CHAPTER 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 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 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 $$F(D)$$
 * 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
 * 47. General Integral by Quadratures
 * 48. The Euler Linear Equation
 * 49. The Laplace Linear Equation
 * 50. Variation of Parameters
 * 51. Linear Systems with Constant Coefficients


 * CHAPTER 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 $$P_n \left({x}\right)$$
 * 56. Solution for Large Values of $$\left|{x}\right|$$
 * 6%. The Bessel Equation and the Function $$J_n \left({x}\right)$$
 * 58. The Function $$Y_n \left({x}\right)$$


 * EXAMPLES
 * SOLUTIONS
 * CODEX