A Treatise on Differential Equations, Volumen1Macmillan and Company, 1877 - 496 páginas |
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Página 86
... proposed . The following is an example . Required the conditions under which the equation Pydx + ( y + Q ) dy = 0 admits of being made integrable by a factor of the form 3 1 y3 + Ry2 + Sy ' P , Q , R and S being functions of x . In the ...
... proposed . The following is an example . Required the conditions under which the equation Pydx + ( y + Q ) dy = 0 admits of being made integrable by a factor of the form 3 1 y3 + Ry2 + Sy ' P , Q , R and S being functions of x . In the ...
Página 117
... proposed diffe- rential equation is of the second degree , and therefore express- ible in the form -P2 ) = 0 . Suppose that the ( dy - p . ) ( dy - p2 ) dx integral V1 = c , is derived from the equation 1 means of an integrating factor ...
... proposed diffe- rential equation is of the second degree , and therefore express- ible in the form -P2 ) = 0 . Suppose that the ( dy - p . ) ( dy - p2 ) dx integral V1 = c , is derived from the equation 1 means of an integrating factor ...
Página 127
... proposed function of p by t , we may form a differential equation be- tween either of the primitive variables and t . Such a diffe- rential equation will necessarily be linear with respect to the primitive variable retained , and its ...
... proposed function of p by t , we may form a differential equation be- tween either of the primitive variables and t . Such a diffe- rential equation will necessarily be linear with respect to the primitive variable retained , and its ...
Página 141
... propose then to deter- mine c as variable , but as so varying that the resulting relation between x and y shall continue to satisfy the differ- ential equation . The general effect of the conversion of c into a function of x or of y ...
... propose then to deter- mine c as variable , but as so varying that the resulting relation between x and y shall continue to satisfy the differ- ential equation . The general effect of the conversion of c into a function of x or of y ...
Página 142
... proposed equation , we have x2 + c2x2 = 1 , whence c = √ ( 1 − x2 ) OC This value of c substituted in y = cx , converts it into y = √√ ( 1 − x2 ) , - which is equivalent to x2 + y2 = 1 . 3. Let us now enquire what determination of ...
... proposed equation , we have x2 + c2x2 = 1 , whence c = √ ( 1 − x2 ) OC This value of c substituted in y = cx , converts it into y = √√ ( 1 − x2 ) , - which is equivalent to x2 + y2 = 1 . 3. Let us now enquire what determination of ...
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Términos y frases comunes
2ndly algebraic arbitrary constant arbitrary function assume C₁ C₂ Cambridge Chap Chapter College complete primitive condition Crown 8vo curve d²u deduce derived determined differential coefficients dp dq dp dy dv dv dx dx dx dy dx dz dx² dy 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 partial differential equation particular integral primitive equation Professor Prop reduced relation represent respect result satisfied second member second order Shew shewn singular solution substituting suppose theorem tion transformation V₁ V₂ whence X₁ Y₁ аф
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