UP
An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Nasser M. Abbasi
January 4, 2023
Compiled on January 4, 2023 at 2:34pm
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Chapter 2, differential equations of the first order and the first degree. Article 8. Exact differential equations. Page 11
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Chapter 2, differential equations of the first order and the first degree. Article 9. Variables searated or separable. Page 13
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Chapter 2, differential equations of the first order and the first degree. Article 10. Homogeneous equations. Page 15
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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
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Chapter 2, differential equations of the first order and the first degree. Article 12. Equations of form \(y f_1(x y)+x f_2( xy) y'=0\). Page 18
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Chapter 2, differential equations of the first order and the first degree. Article 13. Linear equations of first order. Page 19
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Chapter 2, differential equations of the first order and the first degree. Article 14. Equations reducible to linear equations (Bernoulli). Page 21
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Chapter 2, differential equations of the first order and the first degree. Article 15. Page 22
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Chapter 2, differential equations of the first order and the first degree. Article 16. Integrating factors by inspection. Page 23
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Chapter 2, differential equations of the first order and the first degree. Article 17. Other forms which Integrating factors can be found. Page 25
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Chapter 2, differential equations of the first order and the first degree. Article 18. Transformation of variables. Page 26
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Chapter 2, differential equations of the first order and the first degree. Article 19. Summary. Page 29
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Chapter IV, differential equations of the first order and higher degree than the first. Article 24. Equations solvable for \(p\). Page 49
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Chapter IV, differential equations of the first order and higher degree than the first. Article 25. Equations solvable for \(y\). Page 52
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Chapter IV, differential equations of the first order and higher degree than the first. Article 26. Equations solvable for \(x\). Page 55
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Chapter IV, differential equations of the first order and higher degree than the first. Article 27. Clairaut equation. Page 56
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Chapter IV, differential equations of the first order and higher degree than the first. Article 28. Summary. Page 59
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Chapter V, Singular solutions. Article 30. Page 63
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Chapter V, Singular solutions. Article 32. Page 69
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Chapter V, Singular solutions. Article 33. Page 73
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Chapter VII, Linear differential equations with constant coefficients. Article 43. Page 92
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Chapter VII, Linear differential equations with constant coefficients. Article 44. Roots of auxiliary equation repeated. Page 94
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Chapter VII, Linear differential equations with constant coefficients. Article 45. Roots of auxiliary equation complex. Page 95
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Chapter VII, Linear differential equations with constant coefficients. Article 47. Particular integral. Page 100
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Chapter VII, Linear differential equations with constant coefficients. Article 48. Page 103
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Chapter VII, Linear differential equations with constant coefficients. Article 49. Variation of parameters. Page 106
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Chapter VII, Linear differential equations with constant coefficients. Article 50. Method of undetermined coefficients. Page 107
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Chapter VII, Linear differential equations with constant coefficients. Article 51. Cauchy linear equation. Page 114
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Chapter VII, Linear differential equations with constant coefficients. Article 52. Summary. Page 117
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Chapter VIII, Linear differential equations of the second order. Article 53. Change of dependent variable. Page 125
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Chapter VIII, Linear differential equations of the second order. Article 54. Change of independent variable. Page 127
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Chapter VIII, Linear differential equations of the second order. Article 55. Summary. Page 129
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Chapter IX, Miscellaneous methods for solving equations of higher order than first. Article 57. Dependent variable absent. Page 132
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Chapter IX, Miscellaneous methods for solving equations of higher order than first. Article 58. Independent variable absent. Page 135
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Chapter IX, Miscellaneous methods for solving equations of higher order than first. Article 59. Linear equations with particular integral known. Page 136
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Chapter IX, Miscellaneous methods for solving equations of higher order than first. Article 60. Exact equation. Integrating factor. Page 139
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Chapter IX, Miscellaneous methods for solving equations of higher order than first. Article 61. Transformation of variables. Page 143