A Treatise on Differential Equations |
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Page 10
... df ( x , c ) and = da dx dy_df ( x , c ) , df ( x , c ) dc dx dx + dc dx can be equivalent when c is variable , are ( 1 ) when df ( x , c ) dc = = 0 , ( 2 ) when df ( x , c ) = ∞ ; dx dy dx in the latter case = : 00 , and therefore ...
... df ( x , c ) and = da dx dy_df ( x , c ) , df ( x , c ) dc dx dx + dc dx can be equivalent when c is variable , are ( 1 ) when df ( x , c ) dc = = 0 , ( 2 ) when df ( x , c ) = ∞ ; dx dy dx in the latter case = : 00 , and therefore ...
Page 13
... df ( a , c ) = 0 is equivalent to determining dc what particular primitive has contact with the envelope at that point of the latter which corresponds to a given value of x . One important remark yet remains . The elimination of c ...
... df ( a , c ) = 0 is equivalent to determining dc what particular primitive has contact with the envelope at that point of the latter which corresponds to a given value of x . One important remark yet remains . The elimination of c ...
Page 14
George Boole. sense above explained . For it is possible that the derived equation df ( x , c ) - 0 dc may neither on the one hand enable us to determine c as a function of x , so leading to a singular solution ; nor , on the other hand ...
George Boole. sense above explained . For it is possible that the derived equation df ( x , c ) - 0 dc may neither on the one hand enable us to determine c as a function of x , so leading to a singular solution ; nor , on the other hand ...
Page 28
... dF ( x , u ) , dF ( x , u ) du + da = 0 , du dx we have if for brevity we represent F ( x , u ) by F , dF du dx dx du น dF therefore So far , u ) du du du . dF dx Now u = 0 being a singular solution , F ( x , 0 ) is not a con- stant ...
... dF ( x , u ) , dF ( x , u ) du + da = 0 , du dx we have if for brevity we represent F ( x , u ) by F , dF du dx dx du น dF therefore So far , u ) du du du . dF dx Now u = 0 being a singular solution , F ( x , 0 ) is not a con- stant ...
Page 29
... dF dF du dx น dF du = H du fan du , 0 where H is some value intermediate between the greatest and 1 least values which assumes within the limits of integra- dF dx tion . When these limits are , as in the above case , infinitesi- mal ...
... dF dF du dx น dF du = H du fan du , 0 where H is some value intermediate between the greatest and 1 least values which assumes within the limits of integra- dF dx tion . When these limits are , as in the above case , infinitesi- mal ...
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Common terms and phrases
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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