A Treatise on Differential Equations, Τόμος 2Macmillan and Company, 1865 |
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Σελίδα 23
... multiplied by a rational and entire func- tion of logy . It is easy to see that all the higher differential coefficients of y hence derived will possess the same character . And all such vanish with y . We can therefore neither affirm ...
... multiplied by a rational and entire func- tion of logy . It is easy to see that all the higher differential coefficients of y hence derived will possess the same character . And all such vanish with y . We can therefore neither affirm ...
Σελίδα 41
... multiplied by known functions of x . The result of substitution of these values in the given differential equation will therefore consist also of two classes of terms , viz . terms under the sign of summation , which will be the same in ...
... multiplied by known functions of x . The result of substitution of these values in the given differential equation will therefore consist also of two classes of terms , viz . terms under the sign of summation , which will be the same in ...
Σελίδα 75
... Multiplying these equations by the arbitrary constants λη , λης ...... λα respectively , and adding the results , we have 7 dP λα dP + λs do2 dx 11 dP + λn dxn dP ...... + λ4η ) dxn + 1 + . .... 17 dP = 0 ....... ( 2 ) , dxntr a single ...
... Multiplying these equations by the arbitrary constants λη , λης ...... λα respectively , and adding the results , we have 7 dP λα dP + λs do2 dx 11 dP + λn dxn dP ...... + λ4η ) dxn + 1 + . .... 17 dP = 0 ....... ( 2 ) , dxntr a single ...
Σελίδα 99
... the summation with respect toj extending from j = 1 to j = n inclusive . do From the first of equations ( 7 ) multiplied by subtract dpi dF 2 and sum the result with respect 1 to 7-2 ART . 3. ] 99 EQUATIONS OF THE FIRST ORDER .
... the summation with respect toj extending from j = 1 to j = n inclusive . do From the first of equations ( 7 ) multiplied by subtract dpi dF 2 and sum the result with respect 1 to 7-2 ART . 3. ] 99 EQUATIONS OF THE FIRST ORDER .
Σελίδα 100
... multiplied by dpi to i from = ( dF do dF do Σ - We have \ dx¡ dp 、 dp¡ dxi = - Σ.Σ ( dF do dp , dp ; dp , dx ; -- dF do dp dp , dp ; dx . dpi ( 8 ) . The expression under the double sign of summation in the second member vanishes when ...
... multiplied by dpi to i from = ( dF do dF do Σ - We have \ dx¡ dp 、 dp¡ dxi = - Σ.Σ ( dF do dp , dp ; dp , dx ; -- dF do dp dp , dp ; dx . dpi ( 8 ) . The expression under the double sign of summation in the second member vanishes when ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
arbitrary constants C₂ Chap Chapter cloth common integral complete primitive condition Crelle's Journal Crown 8vo deduce derived determine dF dF dF dF dp dFdF differential coefficients dp dp dx dp dq dp dy dp₁ dq dp du₁ dx dp dx dx dx dz dx₁ dx² dy dp dy dx dy dz dz dy dz dz eliminate equa expression Extra fcap factor Fcap given equation Heir of Redclyffe Hence HENRY KINGSLEY homogeneous function independent variables infinite Jacobi JAMES MCCOSH Last Multiplier linear partial differential m₁ memoir obtain ordinary differential equations P₁ partial differential equation particular integral Professor Boole proposition reduced represent result Second Edition shewn singular solution system of ordinary theorem theory tion transformation u₁ u₂ values vanish whence x₁ Y₁ аф
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