A Treatise on Differential Equations, Volum 1Macmillan, 1872 - 85 sider |
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Resultat 1-5 av 31
Side xiii
... positive and negative marks , 139 , 140. Deriva- tion of the singular solution from the complete primitive , 141 . General theorem , 148. Geometrical interpretation , 152. Deri- vation of the singular solution from the differential ...
... positive and negative marks , 139 , 140. Deriva- tion of the singular solution from the complete primitive , 141 . General theorem , 148. Geometrical interpretation , 152. Deri- vation of the singular solution from the differential ...
Side 93
... positive integer . x " For let y = A + Y1 , y , being a new variable which is to replace y , and A a constant whose value is yet to be deter- mined . On substitution and arrangement of the terms we have -aA + b2 + ( na + 2bA ) + b x ...
... positive integer . x " For let y = A + Y1 , y , being a new variable which is to replace y , and A a constant whose value is yet to be deter- mined . On substitution and arrangement of the terms we have -aA + b2 + ( na + 2bA ) + b x ...
Side 95
... positive 7. Let us now examine the form in which the solution is presented . If n 2a 2n = i , which is the condition arrived at in Art . 5 , we have the series of transformations y = Y1 Y2 = = n a x " + b Y1 > a + n + C a + 2n Ya + " b ...
... positive 7. Let us now examine the form in which the solution is presented . If n 2a 2n = i , which is the condition arrived at in Art . 5 , we have the series of transformations y = Y1 Y2 = = n a x " + b Y1 > a + n + C a + 2n Ya + " b ...
Side 96
... positive integer , the solution of the -ay + by = ca " will be expressed in the form of a continued fraction by ( A ) , the value of y ; in the last denomi- nator being given by the solution of the exact differential equa- tion ( B ) or ...
... positive integer , the solution of the -ay + by = ca " will be expressed in the form of a continued fraction by ( A ) , the value of y ; in the last denomi- nator being given by the solution of the exact differential equa- tion ( B ) or ...
Side 97
... positive integer , the solution of ; -ay + by3 = cx " is expressed by ( D ) , the value of y , in the last denominator being given by the exact differential equation ( E ) or ( F ) according as i is odd or even . Ex . Given x B. D. E. ...
... positive integer , the solution of ; -ay + by3 = cx " is expressed by ( D ) , the value of y , in the last denominator being given by the exact differential equation ( E ) or ( F ) according as i is odd or even . Ex . Given x B. D. E. ...
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A Treatise on Differential Equations: Supplementary Volume George Boole Uten tilgangsbegrensning - 1865 |
Vanlige uttrykk og setninger
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