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Chapter 56
An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
56.1
Chapter 2, differential equations of the first order and the first degree. Article 8. Exact differential equations. Page 11
56.2
Chapter 2, differential equations of the first order and the first degree. Article 9. Variables searated or separable. Page 13
56.3
Chapter 2, differential equations of the first order and the first degree. Article 10. Homogeneous equations. Page 15
56.4
Chapter 2, differential equations of the first order and the first degree. Article 11. Equations in which M and N are linear but not homogeneous. Page 16
56.5
Chapter 2, differential equations of the first order and the first degree. Article 12. Page 18
56.6
Chapter 2, differential equations of the first order and the first degree. Article 13. Linear equations of first order. Page 19
56.7
Chapter 2, differential equations of the first order and the first degree. Article 14. Equations reducible to linear equations (Bernoulli). Page 21
56.8
Chapter 2, differential equations of the first order and the first degree. Article 15. Page 22
56.9
Chapter 2, differential equations of the first order and the first degree. Article 16. Integrating factors by inspection. Page 23
56.10
Chapter 2, differential equations of the first order and the first degree. Article 17. Other forms which Integrating factors can be found. Page 25
56.11
Chapter 2, differential equations of the first order and the first degree. Article 18. Transformation of variables. Page 26
56.12
Chapter 2, differential equations of the first order and the first degree. Article 19. Summary. Page 29
56.13
Chapter IV, differential equations of the first order and higher degree than the first. Article 24. Equations solvable for
\(p\)
. Page 49
56.14
Chapter IV, differential equations of the first order and higher degree than the first. Article 25. Equations solvable for
\(y\)
. Page 52
56.15
Chapter IV, differential equations of the first order and higher degree than the first. Article 26. Equations solvable for
\(x\)
. Page 55
56.16
Chapter IV, differential equations of the first order and higher degree than the first. Article 27. Clairaut equation. Page 56
56.17
Chapter IV, differential equations of the first order and higher degree than the first. Article 28. Summary. Page 59
56.18
Chapter V, Singular solutions. Article 30. Page 63
56.19
Chapter V, Singular solutions. Article 32. Page 69
56.20
Chapter V, Singular solutions. Article 33. Page 73
56.21
Chapter VII, Linear differential equations with constant coefficients. Article 43. Page 92
56.22
Chapter VII, Linear differential equations with constant coefficients. Article 44. Roots of auxiliary equation repeated. Page 94
56.23
Chapter VII, Linear differential equations with constant coefficients. Article 45. Roots of auxiliary equation complex. Page 95
56.24
Chapter VII, Linear differential equations with constant coefficients. Article 47. Particular integral. Page 100
56.25
Chapter VII, Linear differential equations with constant coefficients. Article 48. Page 103
56.26
Chapter VII, Linear differential equations with constant coefficients. Article 49. Variation of parameters. Page 106
56.27
Chapter VII, Linear differential equations with constant coefficients. Article 50. Method of undetermined coefficients. Page 107
56.28
Chapter VII, Linear differential equations with constant coefficients. Article 51. Cauchy linear equation. Page 114
56.29
Chapter VII, Linear differential equations with constant coefficients. Article 52. Summary. Page 117
56.30
Chapter VIII, Linear differential equations of the second order. Article 53. Change of dependent variable. Page 125
56.31
Chapter VIII, Linear differential equations of the second order. Article 54. Change of independent variable. Page 127
56.32
Chapter VIII, Linear differential equations of the second order. Article 55. Summary. Page 129
56.33
Chapter IX, Miscellaneous methods for solving equations of higher order than first. Article 57. Dependent variable absent. Page 132
56.34
Chapter IX, Miscellaneous methods for solving equations of higher order than first. Article 58. Independent variable absent. Page 135
56.35
Chapter IX, Miscellaneous methods for solving equations of higher order than first. Article 59. Linear equations with particular integral known. Page 136
56.36
Chapter IX, Miscellaneous methods for solving equations of higher order than first. Article 60. Exact equation. Integrating factor. Page 139
56.37
Chapter IX, Miscellaneous methods for solving equations of higher order than first. Article 61. Transformation of variables. Page 143
56.38
Chapter IX, Miscellaneous methods for solving equations of higher order than first. Article 62. Summary. Page 144
56.39
Chapter X, System of simulataneous equations. Article 64. Systems of linear equations with constant coefficients. Page 150
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