A Treatise on Differential Equations, Volume 1 |
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Page vi
... linear partial differential equations of the first order ; and this , again , properly precedes that of partial differential equations of the first order which are not linear . And in this natural order were the theories of these ...
... linear partial differential equations of the first order ; and this , again , properly precedes that of partial differential equations of the first order which are not linear . And in this natural order were the theories of these ...
Page xi
... Linear equations of first order , 38 . Other forms , 40. Solution by development , 41. Exercises , 44 . 23 CHAPTER III . EXACT DIFFERENTIAL EQUATIONS OF THE FIRST DEGREE 47 General criterion , 47. Mode of solution , 50. Practical ...
... Linear equations of first order , 38 . Other forms , 40. Solution by development , 41. Exercises , 44 . 23 CHAPTER III . EXACT DIFFERENTIAL EQUATIONS OF THE FIRST DEGREE 47 General criterion , 47. Mode of solution , 50. Practical ...
Page xii
... linear , 103. Euler's equation , 104 . 107. Exercises , 110 . - ay + by2 = cx " , 92. Solu- Riccati's equation made Theorem of development , PAGE 55 69 91 CHAPTER VII . ON DIFFERENTIAL EQUATIONS OF THE FIRST ORDER , BUT NOT OF THE FIRST ...
... linear , 103. Euler's equation , 104 . 107. Exercises , 110 . - ay + by2 = cx " , 92. Solu- Riccati's equation made Theorem of development , PAGE 55 69 91 CHAPTER VII . ON DIFFERENTIAL EQUATIONS OF THE FIRST ORDER , BUT NOT OF THE FIRST ...
Page xiii
... Linear equations , 192-199 . General rule when the second Second member a function of x , -Variation Dependent class , 203 , Properties of linear Analogy with Algebraic equations , 206. Exer- member is 0 , 200 . of parameters , ib ...
... Linear equations , 192-199 . General rule when the second Second member a function of x , -Variation Dependent class , 203 , Properties of linear Analogy with Algebraic equations , 206. Exer- member is 0 , 200 . of parameters , ib ...
Page xiv
... Linear equations of first order , 324 . Their genesis , 325. Their solution , 329. Non - linear equations of the first order , 335. Complete primitive , general primitive , and singular solution , 339. Sufficiency of a single complete ...
... Linear equations of first order , 324 . Their genesis , 325. Their solution , 329. Non - linear equations of the first order , 335. Complete primitive , general primitive , and singular solution , 339. Sufficiency of a single complete ...
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Common terms and phrases
2ndly algebraic arbitrary constant arbitrary function assume C₁ C₂ Cambridge Chap Chapter College complete primitive condition corresponding Crown 8vo curve deduce degree derived determined differential coefficients dp dy dv dv dx dx dx dy dy dx dz dx² dy dx dy dz dz dx dz dz Edition eliminating equa exact differential expressed Extra fcap fcap finite given equation Hence homogeneous functions Illustrations independent variable infinite integrating factor involving Mdx+Ndy method Mx+Ny obtained ordinary differential equations P₁ partial differential equation particular integral primitive equation Professor Prop reduced relation represent respect result satisfied second member second order Shew singular solution substituting suppose Taylor's theorem theorem tion transformation V₁ whence y₁ аф
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