A Treatise on Differential EquationsMacmillan, 1865 - 496 σελίδες |
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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 λι , λες λα ....... respectively , and adding the results , we have dP Xx dx s dP + λx dxz 2 dP ..... + λn dxn dP ...... + λn Am ) dxn + 1 11 + ...... 1r dP dxn + r = 0 ........ ( 2 ) ...
... Multiplying these equations by the arbitrary constants λι , λες λα ....... respectively , and adding the results , we have dP Xx dx s dP + λx dxz 2 dP ..... + λn dxn dP ...... + λn Am ) dxn + 1 11 + ...... 1r dP dxn + r = 0 ........ ( 2 ) ...
Σελίδα 99
... multiplied by subtract dpi dF the second multiplied by dp , and sum the 7-2 ART . 3. ] 99 EQUATIONS OF THE FIRST ORDER .
... multiplied by subtract dpi dF the second multiplied by dp , and sum the 7-2 ART . 3. ] 99 EQUATIONS OF THE FIRST ORDER .
Σελίδα 100
George Boole. dF the second multiplied by dp , and sum the result with respect dpi ' to i from i = 1 to i = n inclusive . We have dF do dF do Σ \ dx dp dp dx . ΣΣ ( dF do dp ; _dF do dp , dp ; dp 、 dx , dp 、 dp ; dx . ( 8 ) . The ...
George Boole. dF the second multiplied by dp , and sum the result with respect dpi ' to i from i = 1 to i = n inclusive . We have dF do dF do Σ \ dx dp dp dx . ΣΣ ( dF do dp ; _dF do dp , dp ; dp 、 dx , dp 、 dp ; dx . ( 8 ) . The ...
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arbitrary constants Cambridge Chap Chapter College complete primitive condition Crelle's Journal Crown 8vo deduce derived determine dF dF dF dF dF dF dp dF dx dFdF differential coefficients dp dF dp dp dx dp dq dp dy dp₁ dq dp dv dv dx dp dp dx dx dx dy dy dx dz dx₁ dx² dy dp dy dx dy dz dz dy dz dz Edition eliminate equa Eton College expression Extra fcap factor function given equation Hence J. P. MAHAFFY Jacobi Last Multiplier linear partial differential m₁ memoir ordinary differential equations Owens College P₁ partial differential equations particular integral Professor Boole reduced represent result revised School shewn singular solution system of ordinary theorem theory tion transformation u₁ u₂ values vanish whence X₁ Y₁ аф
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