A Treatise on Differential Equations, Τόμος 1Macmillan, 1872 - 85 σελίδες |
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Σελίδα xv
... means of the properties of homogeneous functions , 403. The method generalized , 406 . Exercises , 410 . PAGE 381 CHAPTER XVII . SYMBOLICAL METHODS , CONTINUED Symbolical form of differential equations with variable coefficients , 412 ...
... means of the properties of homogeneous functions , 403. The method generalized , 406 . Exercises , 410 . PAGE 381 CHAPTER XVII . SYMBOLICAL METHODS , CONTINUED Symbolical form of differential equations with variable coefficients , 412 ...
Σελίδα 1
... means of the fundamental con- ception of a limit ; it expresses that ratio by a differential dy coefficient d ; and of that differential coefficient it shews how to determine the varying magnitude or value . Or , again , con- dy dx ...
... means of the fundamental con- ception of a limit ; it expresses that ratio by a differential dy coefficient d ; and of that differential coefficient it shews how to determine the varying magnitude or value . Or , again , con- dy dx ...
Σελίδα 3
... means of the fundamental conception of the limit . When such is the case , the only adequate ex- pression of those conceptions in language is through the me- dium of differential coefficients , the only adequate expression of the truths ...
... means of the fundamental conception of the limit . When such is the case , the only adequate ex- pression of those conceptions in language is through the me- dium of differential coefficients , the only adequate expression of the truths ...
Σελίδα 31
... means of the formula we shall have - dx √ ( 1 − x3 ) - -1 = Ꮎ , = cos1x + const . , cos1x + cos1y = C1 and , taking the cosine of both members , xy — √ { ( 1 − x2 ) ( 1 — y2 ) } = cos C1 The last result may however be reduced to ...
... means of the formula we shall have - dx √ ( 1 − x3 ) - -1 = Ꮎ , = cos1x + const . , cos1x + cos1y = C1 and , taking the cosine of both members , xy — √ { ( 1 − x2 ) ( 1 — y2 ) } = cos C1 The last result may however be reduced to ...
Σελίδα 69
... means of solving it generally , and it will hereafter appear that its general solution would demand a previous general solution of the differential equation Mdx + Ndy = 0 , of which μ is the integrating factor . But there are many cases ...
... means of solving it generally , and it will hereafter appear that its general solution would demand a previous general solution of the differential equation Mdx + Ndy = 0 , of which μ is the integrating factor . But there are many cases ...
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2ndly algebraic arbitrary constants arbitrary function assume C₁ C₂ Chap Chapter complete primitive condition Crown 8vo curve deduce derived determined differential coefficients dp dp dp dq dp dy dt dt dv du dv dv dv dx dx dx dy dy dx dz dx² dy dx dy dz dz dx dz dy dz dz Edition eliminating equa exact differential expressed fcap finite given equation Hence homogeneous functions independent variable integrating factor involving method Mx+Ny obtained ordinary differential equations P₁ partial differential equation particular integral pdx+qdy primitive equation reduced relation represent respect result satisfied second member second order Shew shewn singular solution substituting suppose theorem tion transformation whence X₁ y₁